{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "_cell_guid": "0b9ffbb2-8d33-eb0c-5a42-0733bdc3b74b"
   },
   "source": [
    "**Introduction**\n",
    "\n",
    "This kernel is an attempt to use every trick in the books to unleash the full power of Linear Regression, including a lot of preprocessing and a look at several Regularization algorithms.\n",
    "\n",
    "At the time of writing, it achieves a score of about 0.121 on the public LB, just using regression, no RF, no xgboost, no ensembling etc. All comments/corrections are more than welcome."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "_cell_guid": "2ba3154a-c2aa-3158-1984-63ad2c0c786a",
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Imports\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.model_selection import cross_val_score, train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.linear_model import LinearRegression, RidgeCV, LassoCV, ElasticNetCV\n",
    "from sklearn.metrics import mean_squared_error, make_scorer\n",
    "from scipy.stats import skew\n",
    "from IPython.display import display\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "# Definitions\n",
    "pd.set_option('display.float_format', lambda x: '%.3f' % x)\n",
    "%matplotlib inline\n",
    "#njobs = 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "_cell_guid": "21fa35be-878b-b4f2-ef6e-68dc070b8bfa"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "train : (1460, 81)\n"
     ]
    }
   ],
   "source": [
    "# Get data\n",
    "train = pd.read_csv(\"../input/train.csv\")\n",
    "print(\"train : \" + str(train.shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "_cell_guid": "7133b089-cd03-a56e-e8a4-8928b28a3c99"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There are 0 duplicate IDs for 1460 total entries\n"
     ]
    }
   ],
   "source": [
    "# Check for duplicates\n",
    "idsUnique = len(set(train.Id))\n",
    "idsTotal = train.shape[0]\n",
    "idsDupli = idsTotal - idsUnique\n",
    "print(\"There are \" + str(idsDupli) + \" duplicate IDs for \" + str(idsTotal) + \" total entries\")\n",
    "\n",
    "# Drop Id column\n",
    "train.drop(\"Id\", axis = 1, inplace = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_cell_guid": "be11c1c7-acfe-cb9a-bc81-95d461b884c5"
   },
   "source": [
    "**Preprocessing**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "_cell_guid": "e9e99565-3296-cb48-3cc7-722b94e3fdac"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fV9XgRryGzHD49b79DuAuEdkO/Bq4zF/rgIh8Fbeu1gPc6IM0DKNEsJB7w8hFVU9PIZeP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\npyRxRUREp/wX14mUHDC2V3AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e5a7e6c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Looking for outliers, as indicated in https://ww2.amstat.org/publications/jse/v19n3/decock.pdf\n",
    "plt.scatter(train.GrLivArea, train.SalePrice, c = \"blue\", marker = \"s\")\n",
    "plt.title(\"Looking for outliers\")\n",
    "plt.xlabel(\"GrLivArea\")\n",
    "plt.ylabel(\"SalePrice\")\n",
    "plt.show()\n",
    "\n",
    "train = train[train.GrLivArea < 4000]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_cell_guid": "2ff6d8cc-1f4b-776c-43d7-e9061eb5bed3"
   },
   "source": [
    "There seems to be 2 extreme outliers on the bottom right, really large houses that sold for really cheap. More generally, the author of the dataset recommends removing 'any houses with more than 4000 square feet' from the dataset.  \n",
    "Reference : https://ww2.amstat.org/publications/jse/v19n3/decock.pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "_cell_guid": "523ad216-4972-bf16-9328-722c461d1e98",
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Log transform the target for official scoring\n",
    "train.SalePrice = np.log1p(train.SalePrice)\n",
    "y = train.SalePrice"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_cell_guid": "9b1a5238-976a-e7ab-00d1-0e92f156e407"
   },
   "source": [
    "Taking logs means that errors in predicting expensive houses and cheap houses will affect the result equally."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "_cell_guid": "1fecd55e-0392-4d08-c4f7-da4326f42538",
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Handle missing values for features where median/mean or most common value doesn't make sense\n",
    "\n",
    "# Alley : data description says NA means \"no alley access\"\n",
    "train.loc[:, \"Alley\"] = train.loc[:, \"Alley\"].fillna(\"None\")\n",
    "# BedroomAbvGr : NA most likely means 0\n",
    "train.loc[:, \"BedroomAbvGr\"] = train.loc[:, \"BedroomAbvGr\"].fillna(0)\n",
    "# BsmtQual etc : data description says NA for basement features is \"no basement\"\n",
    "train.loc[:, \"BsmtQual\"] = train.loc[:, \"BsmtQual\"].fillna(\"No\")\n",
    "train.loc[:, \"BsmtCond\"] = train.loc[:, \"BsmtCond\"].fillna(\"No\")\n",
    "train.loc[:, \"BsmtExposure\"] = train.loc[:, \"BsmtExposure\"].fillna(\"No\")\n",
    "train.loc[:, \"BsmtFinType1\"] = train.loc[:, \"BsmtFinType1\"].fillna(\"No\")\n",
    "train.loc[:, \"BsmtFinType2\"] = train.loc[:, \"BsmtFinType2\"].fillna(\"No\")\n",
    "train.loc[:, \"BsmtFullBath\"] = train.loc[:, \"BsmtFullBath\"].fillna(0)\n",
    "train.loc[:, \"BsmtHalfBath\"] = train.loc[:, \"BsmtHalfBath\"].fillna(0)\n",
    "train.loc[:, \"BsmtUnfSF\"] = train.loc[:, \"BsmtUnfSF\"].fillna(0)\n",
    "# CentralAir : NA most likely means No\n",
    "train.loc[:, \"CentralAir\"] = train.loc[:, \"CentralAir\"].fillna(\"N\")\n",
    "# Condition : NA most likely means Normal\n",
    "train.loc[:, \"Condition1\"] = train.loc[:, \"Condition1\"].fillna(\"Norm\")\n",
    "train.loc[:, \"Condition2\"] = train.loc[:, \"Condition2\"].fillna(\"Norm\")\n",
    "# EnclosedPorch : NA most likely means no enclosed porch\n",
    "train.loc[:, \"EnclosedPorch\"] = train.loc[:, \"EnclosedPorch\"].fillna(0)\n",
    "# External stuff : NA most likely means average\n",
    "train.loc[:, \"ExterCond\"] = train.loc[:, \"ExterCond\"].fillna(\"TA\")\n",
    "train.loc[:, \"ExterQual\"] = train.loc[:, \"ExterQual\"].fillna(\"TA\")\n",
    "# Fence : data description says NA means \"no fence\"\n",
    "train.loc[:, \"Fence\"] = train.loc[:, \"Fence\"].fillna(\"No\")\n",
    "# FireplaceQu : data description says NA means \"no fireplace\"\n",
    "train.loc[:, \"FireplaceQu\"] = train.loc[:, \"FireplaceQu\"].fillna(\"No\")\n",
    "train.loc[:, \"Fireplaces\"] = train.loc[:, \"Fireplaces\"].fillna(0)\n",
    "# Functional : data description says NA means typical\n",
    "train.loc[:, \"Functional\"] = train.loc[:, \"Functional\"].fillna(\"Typ\")\n",
    "# GarageType etc : data description says NA for garage features is \"no garage\"\n",
    "train.loc[:, \"GarageType\"] = train.loc[:, \"GarageType\"].fillna(\"No\")\n",
    "train.loc[:, \"GarageFinish\"] = train.loc[:, \"GarageFinish\"].fillna(\"No\")\n",
    "train.loc[:, \"GarageQual\"] = train.loc[:, \"GarageQual\"].fillna(\"No\")\n",
    "train.loc[:, \"GarageCond\"] = train.loc[:, \"GarageCond\"].fillna(\"No\")\n",
    "train.loc[:, \"GarageArea\"] = train.loc[:, \"GarageArea\"].fillna(0)\n",
    "train.loc[:, \"GarageCars\"] = train.loc[:, \"GarageCars\"].fillna(0)\n",
    "# HalfBath : NA most likely means no half baths above grade\n",
    "train.loc[:, \"HalfBath\"] = train.loc[:, \"HalfBath\"].fillna(0)\n",
    "# HeatingQC : NA most likely means typical\n",
    "train.loc[:, \"HeatingQC\"] = train.loc[:, \"HeatingQC\"].fillna(\"TA\")\n",
    "# KitchenAbvGr : NA most likely means 0\n",
    "train.loc[:, \"KitchenAbvGr\"] = train.loc[:, \"KitchenAbvGr\"].fillna(0)\n",
    "# KitchenQual : NA most likely means typical\n",
    "train.loc[:, \"KitchenQual\"] = train.loc[:, \"KitchenQual\"].fillna(\"TA\")\n",
    "# LotFrontage : NA most likely means no lot frontage\n",
    "train.loc[:, \"LotFrontage\"] = train.loc[:, \"LotFrontage\"].fillna(0)\n",
    "# LotShape : NA most likely means regular\n",
    "train.loc[:, \"LotShape\"] = train.loc[:, \"LotShape\"].fillna(\"Reg\")\n",
    "# MasVnrType : NA most likely means no veneer\n",
    "train.loc[:, \"MasVnrType\"] = train.loc[:, \"MasVnrType\"].fillna(\"None\")\n",
    "train.loc[:, \"MasVnrArea\"] = train.loc[:, \"MasVnrArea\"].fillna(0)\n",
    "# MiscFeature : data description says NA means \"no misc feature\"\n",
    "train.loc[:, \"MiscFeature\"] = train.loc[:, \"MiscFeature\"].fillna(\"No\")\n",
    "train.loc[:, \"MiscVal\"] = train.loc[:, \"MiscVal\"].fillna(0)\n",
    "# OpenPorchSF : NA most likely means no open porch\n",
    "train.loc[:, \"OpenPorchSF\"] = train.loc[:, \"OpenPorchSF\"].fillna(0)\n",
    "# PavedDrive : NA most likely means not paved\n",
    "train.loc[:, \"PavedDrive\"] = train.loc[:, \"PavedDrive\"].fillna(\"N\")\n",
    "# PoolQC : data description says NA means \"no pool\"\n",
    "train.loc[:, \"PoolQC\"] = train.loc[:, \"PoolQC\"].fillna(\"No\")\n",
    "train.loc[:, \"PoolArea\"] = train.loc[:, \"PoolArea\"].fillna(0)\n",
    "# SaleCondition : NA most likely means normal sale\n",
    "train.loc[:, \"SaleCondition\"] = train.loc[:, \"SaleCondition\"].fillna(\"Normal\")\n",
    "# ScreenPorch : NA most likely means no screen porch\n",
    "train.loc[:, \"ScreenPorch\"] = train.loc[:, \"ScreenPorch\"].fillna(0)\n",
    "# TotRmsAbvGrd : NA most likely means 0\n",
    "train.loc[:, \"TotRmsAbvGrd\"] = train.loc[:, \"TotRmsAbvGrd\"].fillna(0)\n",
    "# Utilities : NA most likely means all public utilities\n",
    "train.loc[:, \"Utilities\"] = train.loc[:, \"Utilities\"].fillna(\"AllPub\")\n",
    "# WoodDeckSF : NA most likely means no wood deck\n",
    "train.loc[:, \"WoodDeckSF\"] = train.loc[:, \"WoodDeckSF\"].fillna(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "_cell_guid": "f9de2ccc-4a07-a8f2-75d8-5151ff653e86",
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Some numerical features are actually really categories\n",
    "train = train.replace({\"MSSubClass\" : {20 : \"SC20\", 30 : \"SC30\", 40 : \"SC40\", 45 : \"SC45\", \n",
    "                                       50 : \"SC50\", 60 : \"SC60\", 70 : \"SC70\", 75 : \"SC75\", \n",
    "                                       80 : \"SC80\", 85 : \"SC85\", 90 : \"SC90\", 120 : \"SC120\", \n",
    "                                       150 : \"SC150\", 160 : \"SC160\", 180 : \"SC180\", 190 : \"SC190\"},\n",
    "                       \"MoSold\" : {1 : \"Jan\", 2 : \"Feb\", 3 : \"Mar\", 4 : \"Apr\", 5 : \"May\", 6 : \"Jun\",\n",
    "                                   7 : \"Jul\", 8 : \"Aug\", 9 : \"Sep\", 10 : \"Oct\", 11 : \"Nov\", 12 : \"Dec\"}\n",
    "                      })"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "_cell_guid": "3c57fec5-4eb9-9130-cf96-54e00275a594",
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Encode some categorical features as ordered numbers when there is information in the order\n",
    "train = train.replace({\"Alley\" : {\"Grvl\" : 1, \"Pave\" : 2},\n",
    "                       \"BsmtCond\" : {\"No\" : 0, \"Po\" : 1, \"Fa\" : 2, \"TA\" : 3, \"Gd\" : 4, \"Ex\" : 5},\n",
    "                       \"BsmtExposure\" : {\"No\" : 0, \"Mn\" : 1, \"Av\": 2, \"Gd\" : 3},\n",
    "                       \"BsmtFinType1\" : {\"No\" : 0, \"Unf\" : 1, \"LwQ\": 2, \"Rec\" : 3, \"BLQ\" : 4, \n",
    "                                         \"ALQ\" : 5, \"GLQ\" : 6},\n",
    "                       \"BsmtFinType2\" : {\"No\" : 0, \"Unf\" : 1, \"LwQ\": 2, \"Rec\" : 3, \"BLQ\" : 4, \n",
    "                                         \"ALQ\" : 5, \"GLQ\" : 6},\n",
    "                       \"BsmtQual\" : {\"No\" : 0, \"Po\" : 1, \"Fa\" : 2, \"TA\": 3, \"Gd\" : 4, \"Ex\" : 5},\n",
    "                       \"ExterCond\" : {\"Po\" : 1, \"Fa\" : 2, \"TA\": 3, \"Gd\": 4, \"Ex\" : 5},\n",
    "                       \"ExterQual\" : {\"Po\" : 1, \"Fa\" : 2, \"TA\": 3, \"Gd\": 4, \"Ex\" : 5},\n",
    "                       \"FireplaceQu\" : {\"No\" : 0, \"Po\" : 1, \"Fa\" : 2, \"TA\" : 3, \"Gd\" : 4, \"Ex\" : 5},\n",
    "                       \"Functional\" : {\"Sal\" : 1, \"Sev\" : 2, \"Maj2\" : 3, \"Maj1\" : 4, \"Mod\": 5, \n",
    "                                       \"Min2\" : 6, \"Min1\" : 7, \"Typ\" : 8},\n",
    "                       \"GarageCond\" : {\"No\" : 0, \"Po\" : 1, \"Fa\" : 2, \"TA\" : 3, \"Gd\" : 4, \"Ex\" : 5},\n",
    "                       \"GarageQual\" : {\"No\" : 0, \"Po\" : 1, \"Fa\" : 2, \"TA\" : 3, \"Gd\" : 4, \"Ex\" : 5},\n",
    "                       \"HeatingQC\" : {\"Po\" : 1, \"Fa\" : 2, \"TA\" : 3, \"Gd\" : 4, \"Ex\" : 5},\n",
    "                       \"KitchenQual\" : {\"Po\" : 1, \"Fa\" : 2, \"TA\" : 3, \"Gd\" : 4, \"Ex\" : 5},\n",
    "                       \"LandSlope\" : {\"Sev\" : 1, \"Mod\" : 2, \"Gtl\" : 3},\n",
    "                       \"LotShape\" : {\"IR3\" : 1, \"IR2\" : 2, \"IR1\" : 3, \"Reg\" : 4},\n",
    "                       \"PavedDrive\" : {\"N\" : 0, \"P\" : 1, \"Y\" : 2},\n",
    "                       \"PoolQC\" : {\"No\" : 0, \"Fa\" : 1, \"TA\" : 2, \"Gd\" : 3, \"Ex\" : 4},\n",
    "                       \"Street\" : {\"Grvl\" : 1, \"Pave\" : 2},\n",
    "                       \"Utilities\" : {\"ELO\" : 1, \"NoSeWa\" : 2, \"NoSewr\" : 3, \"AllPub\" : 4}}\n",
    "                     )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_cell_guid": "5fedb3e5-d6e0-efdd-d92a-8079377f82a9"
   },
   "source": [
    "Then we will create new features, in 3 ways : \n",
    "\n",
    " 1. Simplifications of existing features\n",
    " 2. Combinations of existing features\n",
    " 3. Polynomials on the top 10 existing features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "_cell_guid": "10327932-cac0-9310-1041-4572e72b44eb",
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Create new features\n",
    "# 1* Simplifications of existing features\n",
    "train[\"SimplOverallQual\"] = train.OverallQual.replace({1 : 1, 2 : 1, 3 : 1, # bad\n",
    "                                                       4 : 2, 5 : 2, 6 : 2, # average\n",
    "                                                       7 : 3, 8 : 3, 9 : 3, 10 : 3 # good\n",
    "                                                      })\n",
    "train[\"SimplOverallCond\"] = train.OverallCond.replace({1 : 1, 2 : 1, 3 : 1, # bad\n",
    "                                                       4 : 2, 5 : 2, 6 : 2, # average\n",
    "                                                       7 : 3, 8 : 3, 9 : 3, 10 : 3 # good\n",
    "                                                      })\n",
    "train[\"SimplPoolQC\"] = train.PoolQC.replace({1 : 1, 2 : 1, # average\n",
    "                                             3 : 2, 4 : 2 # good\n",
    "                                            })\n",
    "train[\"SimplGarageCond\"] = train.GarageCond.replace({1 : 1, # bad\n",
    "                                                     2 : 1, 3 : 1, # average\n",
    "                                                     4 : 2, 5 : 2 # good\n",
    "                                                    })\n",
    "train[\"SimplGarageQual\"] = train.GarageQual.replace({1 : 1, # bad\n",
    "                                                     2 : 1, 3 : 1, # average\n",
    "                                                     4 : 2, 5 : 2 # good\n",
    "                                                    })\n",
    "train[\"SimplFireplaceQu\"] = train.FireplaceQu.replace({1 : 1, # bad\n",
    "                                                       2 : 1, 3 : 1, # average\n",
    "                                                       4 : 2, 5 : 2 # good\n",
    "                                                      })\n",
    "train[\"SimplFireplaceQu\"] = train.FireplaceQu.replace({1 : 1, # bad\n",
    "                                                       2 : 1, 3 : 1, # average\n",
    "                                                       4 : 2, 5 : 2 # good\n",
    "                                                      })\n",
    "train[\"SimplFunctional\"] = train.Functional.replace({1 : 1, 2 : 1, # bad\n",
    "                                                     3 : 2, 4 : 2, # major\n",
    "                                                     5 : 3, 6 : 3, 7 : 3, # minor\n",
    "                                                     8 : 4 # typical\n",
    "                                                    })\n",
    "train[\"SimplKitchenQual\"] = train.KitchenQual.replace({1 : 1, # bad\n",
    "                                                       2 : 1, 3 : 1, # average\n",
    "                                                       4 : 2, 5 : 2 # good\n",
    "                                                      })\n",
    "train[\"SimplHeatingQC\"] = train.HeatingQC.replace({1 : 1, # bad\n",
    "                                                   2 : 1, 3 : 1, # average\n",
    "                                                   4 : 2, 5 : 2 # good\n",
    "                                                  })\n",
    "train[\"SimplBsmtFinType1\"] = train.BsmtFinType1.replace({1 : 1, # unfinished\n",
    "                                                         2 : 1, 3 : 1, # rec room\n",
    "                                                         4 : 2, 5 : 2, 6 : 2 # living quarters\n",
    "                                                        })\n",
    "train[\"SimplBsmtFinType2\"] = train.BsmtFinType2.replace({1 : 1, # unfinished\n",
    "                                                         2 : 1, 3 : 1, # rec room\n",
    "                                                         4 : 2, 5 : 2, 6 : 2 # living quarters\n",
    "                                                        })\n",
    "train[\"SimplBsmtCond\"] = train.BsmtCond.replace({1 : 1, # bad\n",
    "                                                 2 : 1, 3 : 1, # average\n",
    "                                                 4 : 2, 5 : 2 # good\n",
    "                                                })\n",
    "train[\"SimplBsmtQual\"] = train.BsmtQual.replace({1 : 1, # bad\n",
    "                                                 2 : 1, 3 : 1, # average\n",
    "                                                 4 : 2, 5 : 2 # good\n",
    "                                                })\n",
    "train[\"SimplExterCond\"] = train.ExterCond.replace({1 : 1, # bad\n",
    "                                                   2 : 1, 3 : 1, # average\n",
    "                                                   4 : 2, 5 : 2 # good\n",
    "                                                  })\n",
    "train[\"SimplExterQual\"] = train.ExterQual.replace({1 : 1, # bad\n",
    "                                                   2 : 1, 3 : 1, # average\n",
    "                                                   4 : 2, 5 : 2 # good\n",
    "                                                  })\n",
    "\n",
    "# 2* Combinations of existing features\n",
    "# Overall quality of the house\n",
    "train[\"OverallGrade\"] = train[\"OverallQual\"] * train[\"OverallCond\"]\n",
    "# Overall quality of the garage\n",
    "train[\"GarageGrade\"] = train[\"GarageQual\"] * train[\"GarageCond\"]\n",
    "# Overall quality of the exterior\n",
    "train[\"ExterGrade\"] = train[\"ExterQual\"] * train[\"ExterCond\"]\n",
    "# Overall kitchen score\n",
    "train[\"KitchenScore\"] = train[\"KitchenAbvGr\"] * train[\"KitchenQual\"]\n",
    "# Overall fireplace score\n",
    "train[\"FireplaceScore\"] = train[\"Fireplaces\"] * train[\"FireplaceQu\"]\n",
    "# Overall garage score\n",
    "train[\"GarageScore\"] = train[\"GarageArea\"] * train[\"GarageQual\"]\n",
    "# Overall pool score\n",
    "train[\"PoolScore\"] = train[\"PoolArea\"] * train[\"PoolQC\"]\n",
    "# Simplified overall quality of the house\n",
    "train[\"SimplOverallGrade\"] = train[\"SimplOverallQual\"] * train[\"SimplOverallCond\"]\n",
    "# Simplified overall quality of the exterior\n",
    "train[\"SimplExterGrade\"] = train[\"SimplExterQual\"] * train[\"SimplExterCond\"]\n",
    "# Simplified overall pool score\n",
    "train[\"SimplPoolScore\"] = train[\"PoolArea\"] * train[\"SimplPoolQC\"]\n",
    "# Simplified overall garage score\n",
    "train[\"SimplGarageScore\"] = train[\"GarageArea\"] * train[\"SimplGarageQual\"]\n",
    "# Simplified overall fireplace score\n",
    "train[\"SimplFireplaceScore\"] = train[\"Fireplaces\"] * train[\"SimplFireplaceQu\"]\n",
    "# Simplified overall kitchen score\n",
    "train[\"SimplKitchenScore\"] = train[\"KitchenAbvGr\"] * train[\"SimplKitchenQual\"]\n",
    "# Total number of bathrooms\n",
    "train[\"TotalBath\"] = train[\"BsmtFullBath\"] + (0.5 * train[\"BsmtHalfBath\"]) + \\\n",
    "train[\"FullBath\"] + (0.5 * train[\"HalfBath\"])\n",
    "# Total SF for house (incl. basement)\n",
    "train[\"AllSF\"] = train[\"GrLivArea\"] + train[\"TotalBsmtSF\"]\n",
    "# Total SF for 1st + 2nd floors\n",
    "train[\"AllFlrsSF\"] = train[\"1stFlrSF\"] + train[\"2ndFlrSF\"]\n",
    "# Total SF for porch\n",
    "train[\"AllPorchSF\"] = train[\"OpenPorchSF\"] + train[\"EnclosedPorch\"] + \\\n",
    "train[\"3SsnPorch\"] + train[\"ScreenPorch\"]\n",
    "# Has masonry veneer or not\n",
    "train[\"HasMasVnr\"] = train.MasVnrType.replace({\"BrkCmn\" : 1, \"BrkFace\" : 1, \"CBlock\" : 1, \n",
    "                                               \"Stone\" : 1, \"None\" : 0})\n",
    "# House completed before sale or not\n",
    "train[\"BoughtOffPlan\"] = train.SaleCondition.replace({\"Abnorml\" : 0, \"Alloca\" : 0, \"AdjLand\" : 0, \n",
    "                                                      \"Family\" : 0, \"Normal\" : 0, \"Partial\" : 1})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "_cell_guid": "a345817d-8b0c-7467-7524-16a4cbb02794"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Find most important features relative to target\n",
      "SalePrice            1.000\n",
      "OverallQual          0.819\n",
      "AllSF                0.817\n",
      "AllFlrsSF            0.729\n",
      "GrLivArea            0.719\n",
      "SimplOverallQual     0.708\n",
      "ExterQual            0.681\n",
      "GarageCars           0.680\n",
      "TotalBath            0.673\n",
      "KitchenQual          0.667\n",
      "GarageScore          0.657\n",
      "GarageArea           0.655\n",
      "TotalBsmtSF          0.642\n",
      "SimplExterQual       0.636\n",
      "SimplGarageScore     0.631\n",
      "BsmtQual             0.615\n",
      "1stFlrSF             0.614\n",
      "SimplKitchenQual     0.610\n",
      "OverallGrade         0.604\n",
      "SimplBsmtQual        0.594\n",
      "FullBath             0.591\n",
      "YearBuilt            0.589\n",
      "ExterGrade           0.587\n",
      "YearRemodAdd         0.569\n",
      "FireplaceQu          0.547\n",
      "GarageYrBlt          0.544\n",
      "TotRmsAbvGrd         0.533\n",
      "SimplOverallGrade    0.527\n",
      "SimplKitchenScore    0.523\n",
      "FireplaceScore       0.518\n",
      "                     ...  \n",
      "SimplBsmtCond        0.204\n",
      "BedroomAbvGr         0.204\n",
      "AllPorchSF           0.199\n",
      "LotFrontage          0.174\n",
      "SimplFunctional      0.137\n",
      "Functional           0.136\n",
      "ScreenPorch          0.124\n",
      "SimplBsmtFinType2    0.105\n",
      "Street               0.058\n",
      "3SsnPorch            0.056\n",
      "ExterCond            0.051\n",
      "PoolArea             0.041\n",
      "SimplPoolScore       0.040\n",
      "SimplPoolQC          0.040\n",
      "PoolScore            0.040\n",
      "PoolQC               0.038\n",
      "BsmtFinType2         0.016\n",
      "Utilities            0.013\n",
      "BsmtFinSF2           0.006\n",
      "BsmtHalfBath        -0.015\n",
      "MiscVal             -0.020\n",
      "SimplOverallCond    -0.028\n",
      "YrSold              -0.034\n",
      "OverallCond         -0.037\n",
      "LowQualFinSF        -0.038\n",
      "LandSlope           -0.040\n",
      "SimplExterCond      -0.042\n",
      "KitchenAbvGr        -0.148\n",
      "EnclosedPorch       -0.149\n",
      "LotShape            -0.286\n",
      "Name: SalePrice, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# Find most important features relative to target\n",
    "print(\"Find most important features relative to target\")\n",
    "corr = train.corr()\n",
    "corr.sort_values([\"SalePrice\"], ascending = False, inplace = True)\n",
    "print(corr.SalePrice)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "_cell_guid": "bf2a8386-cb11-969a-d5cb-a2bb4a7094fd",
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Create new features\n",
    "# 3* Polynomials on the top 10 existing features\n",
    "train[\"OverallQual-s2\"] = train[\"OverallQual\"] ** 2\n",
    "train[\"OverallQual-s3\"] = train[\"OverallQual\"] ** 3\n",
    "train[\"OverallQual-Sq\"] = np.sqrt(train[\"OverallQual\"])\n",
    "train[\"AllSF-2\"] = train[\"AllSF\"] ** 2\n",
    "train[\"AllSF-3\"] = train[\"AllSF\"] ** 3\n",
    "train[\"AllSF-Sq\"] = np.sqrt(train[\"AllSF\"])\n",
    "train[\"AllFlrsSF-2\"] = train[\"AllFlrsSF\"] ** 2\n",
    "train[\"AllFlrsSF-3\"] = train[\"AllFlrsSF\"] ** 3\n",
    "train[\"AllFlrsSF-Sq\"] = np.sqrt(train[\"AllFlrsSF\"])\n",
    "train[\"GrLivArea-2\"] = train[\"GrLivArea\"] ** 2\n",
    "train[\"GrLivArea-3\"] = train[\"GrLivArea\"] ** 3\n",
    "train[\"GrLivArea-Sq\"] = np.sqrt(train[\"GrLivArea\"])\n",
    "train[\"SimplOverallQual-s2\"] = train[\"SimplOverallQual\"] ** 2\n",
    "train[\"SimplOverallQual-s3\"] = train[\"SimplOverallQual\"] ** 3\n",
    "train[\"SimplOverallQual-Sq\"] = np.sqrt(train[\"SimplOverallQual\"])\n",
    "train[\"ExterQual-2\"] = train[\"ExterQual\"] ** 2\n",
    "train[\"ExterQual-3\"] = train[\"ExterQual\"] ** 3\n",
    "train[\"ExterQual-Sq\"] = np.sqrt(train[\"ExterQual\"])\n",
    "train[\"GarageCars-2\"] = train[\"GarageCars\"] ** 2\n",
    "train[\"GarageCars-3\"] = train[\"GarageCars\"] ** 3\n",
    "train[\"GarageCars-Sq\"] = np.sqrt(train[\"GarageCars\"])\n",
    "train[\"TotalBath-2\"] = train[\"TotalBath\"] ** 2\n",
    "train[\"TotalBath-3\"] = train[\"TotalBath\"] ** 3\n",
    "train[\"TotalBath-Sq\"] = np.sqrt(train[\"TotalBath\"])\n",
    "train[\"KitchenQual-2\"] = train[\"KitchenQual\"] ** 2\n",
    "train[\"KitchenQual-3\"] = train[\"KitchenQual\"] ** 3\n",
    "train[\"KitchenQual-Sq\"] = np.sqrt(train[\"KitchenQual\"])\n",
    "train[\"GarageScore-2\"] = train[\"GarageScore\"] ** 2\n",
    "train[\"GarageScore-3\"] = train[\"GarageScore\"] ** 3\n",
    "train[\"GarageScore-Sq\"] = np.sqrt(train[\"GarageScore\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "_cell_guid": "9a8ce5ba-12b9-61d6-6ae8-d3ff838f082e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Numerical features : 117\n",
      "Categorical features : 26\n"
     ]
    }
   ],
   "source": [
    "# Differentiate numerical features (minus the target) and categorical features\n",
    "categorical_features = train.select_dtypes(include = [\"object\"]).columns\n",
    "numerical_features = train.select_dtypes(exclude = [\"object\"]).columns\n",
    "numerical_features = numerical_features.drop(\"SalePrice\")\n",
    "print(\"Numerical features : \" + str(len(numerical_features)))\n",
    "print(\"Categorical features : \" + str(len(categorical_features)))\n",
    "train_num = train[numerical_features]\n",
    "train_cat = train[categorical_features]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "_cell_guid": "7fed0c33-faa1-e455-c834-7ec12f6d33e5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NAs for numerical features in train : 81\n",
      "Remaining NAs for numerical features in train : 0\n"
     ]
    }
   ],
   "source": [
    "# Handle remaining missing values for numerical features by using median as replacement\n",
    "print(\"NAs for numerical features in train : \" + str(train_num.isnull().values.sum()))\n",
    "train_num = train_num.fillna(train_num.median())\n",
    "print(\"Remaining NAs for numerical features in train : \" + str(train_num.isnull().values.sum()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "_cell_guid": "571b9524-6559-d088-1917-9f290a662af1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "86 skewed numerical features to log transform\n"
     ]
    }
   ],
   "source": [
    "# Log transform of the skewed numerical features to lessen impact of outliers\n",
    "# Inspired by Alexandru Papiu's script : https://www.kaggle.com/apapiu/house-prices-advanced-regression-techniques/regularized-linear-models\n",
    "# As a general rule of thumb, a skewness with an absolute value > 0.5 is considered at least moderately skewed\n",
    "skewness = train_num.apply(lambda x: skew(x))\n",
    "skewness = skewness[abs(skewness) > 0.5]\n",
    "print(str(skewness.shape[0]) + \" skewed numerical features to log transform\")\n",
    "skewed_features = skewness.index\n",
    "train_num[skewed_features] = np.log1p(train_num[skewed_features])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "_cell_guid": "93029443-cbb3-e2ee-9c4a-a61e22ef1a15"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NAs for categorical features in train : 1\n",
      "Remaining NAs for categorical features in train : 0\n"
     ]
    }
   ],
   "source": [
    "# Create dummy features for categorical values via one-hot encoding\n",
    "print(\"NAs for categorical features in train : \" + str(train_cat.isnull().values.sum()))\n",
    "train_cat = pd.get_dummies(train_cat)\n",
    "print(\"Remaining NAs for categorical features in train : \" + str(train_cat.isnull().values.sum()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_cell_guid": "a1ae46d1-8787-67a3-2f69-6497c97320eb"
   },
   "source": [
    "**Modeling**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "_cell_guid": "3685f20a-c332-7ab0-cced-03d639d28833"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "New number of features : 319\n",
      "X_train : (1019, 319)\n",
      "X_test : (437, 319)\n",
      "y_train : (1019,)\n",
      "y_test : (437,)\n"
     ]
    }
   ],
   "source": [
    "# Join categorical and numerical features\n",
    "train = pd.concat([train_num, train_cat], axis = 1)\n",
    "print(\"New number of features : \" + str(train.shape[1]))\n",
    "\n",
    "# Partition the dataset in train + validation sets\n",
    "X_train, X_test, y_train, y_test = train_test_split(train, y, test_size = 0.3, random_state = 0)\n",
    "print(\"X_train : \" + str(X_train.shape))\n",
    "print(\"X_test : \" + str(X_test.shape))\n",
    "print(\"y_train : \" + str(y_train.shape))\n",
    "print(\"y_test : \" + str(y_test.shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "_cell_guid": "1279ec22-61c2-4d5a-b8da-9dcadbda564d"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.5/site-packages/pandas/core/indexing.py:465: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  self.obj[item] = s\n"
     ]
    }
   ],
   "source": [
    "# Standardize numerical features\n",
    "stdSc = StandardScaler()\n",
    "X_train.loc[:, numerical_features] = stdSc.fit_transform(X_train.loc[:, numerical_features])\n",
    "X_test.loc[:, numerical_features] = stdSc.transform(X_test.loc[:, numerical_features])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_cell_guid": "ef95410a-0008-c898-56f4-bde9a683aba5"
   },
   "source": [
    "Standardization cannot be done before  the partitioning, as we don't want to fit the StandardScaler on some observations that will later be used in the test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "_cell_guid": "e06d07c0-b968-f28e-1c2e-389fbc48e9f8",
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define error measure for official scoring : RMSE\n",
    "scorer = make_scorer(mean_squared_error, greater_is_better = False)\n",
    "\n",
    "def rmse_cv_train(model):\n",
    "    rmse= np.sqrt(-cross_val_score(model, X_train, y_train, scoring = scorer, cv = 10))\n",
    "    return(rmse)\n",
    "\n",
    "def rmse_cv_test(model):\n",
    "    rmse= np.sqrt(-cross_val_score(model, X_test, y_test, scoring = scorer, cv = 10))\n",
    "    return(rmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_cell_guid": "72acb8a1-5ee5-ce21-1620-5109e1742197"
   },
   "source": [
    "Note : I'm not getting nearly the same numbers in local CV compared to public LB, so I'm a tad worried that my CV process may have an issue somewhere. If you spot something, please let me know."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_cell_guid": "9fe1c63e-3803-feac-362c-631399fdb8ec"
   },
   "source": [
    "**1* Linear Regression without regularization**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "_cell_guid": "101cf15a-9006-ac9a-8abe-756371fd8b1a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE on Training set : 15758371373.7\n",
      "RMSE on Test set : 0.395779797728\n"
     ]
    },
    {
     "data": {
      "image/png": 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XLt1BacXHjomsoeEaiorOAaL7wdLcvfv8YuP4d3PFFVfwVvzrjjFmZ8bOEdZV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\nhaBFv9ZVAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e957b08d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7OnwamgPearFyW4o/cDaNnbo1n0doTChVBVX6/C5H6nmm8iA3/eHf7l0Ud5c0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\niYUSioiIxOL/AbpcSzRZQlkMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e5a2255c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Linear Regression\n",
    "lr = LinearRegression()\n",
    "lr.fit(X_train, y_train)\n",
    "\n",
    "# Look at predictions on training and validation set\n",
    "print(\"RMSE on Training set :\", rmse_cv_train(lr).mean())\n",
    "print(\"RMSE on Test set :\", rmse_cv_test(lr).mean())\n",
    "y_train_pred = lr.predict(X_train)\n",
    "y_test_pred = lr.predict(X_test)\n",
    "\n",
    "# Plot residuals\n",
    "plt.scatter(y_train_pred, y_train_pred - y_train, c = \"blue\", marker = \"s\", label = \"Training data\")\n",
    "plt.scatter(y_test_pred, y_test_pred - y_test, c = \"lightgreen\", marker = \"s\", label = \"Validation data\")\n",
    "plt.title(\"Linear regression\")\n",
    "plt.xlabel(\"Predicted values\")\n",
    "plt.ylabel(\"Residuals\")\n",
    "plt.legend(loc = \"upper left\")\n",
    "plt.hlines(y = 0, xmin = 10.5, xmax = 13.5, color = \"red\")\n",
    "plt.show()\n",
    "\n",
    "# Plot predictions\n",
    "plt.scatter(y_train_pred, y_train, c = \"blue\", marker = \"s\", label = \"Training data\")\n",
    "plt.scatter(y_test_pred, y_test, c = \"lightgreen\", marker = \"s\", label = \"Validation data\")\n",
    "plt.title(\"Linear regression\")\n",
    "plt.xlabel(\"Predicted values\")\n",
    "plt.ylabel(\"Real values\")\n",
    "plt.legend(loc = \"upper left\")\n",
    "plt.plot([10.5, 13.5], [10.5, 13.5], c = \"red\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_cell_guid": "2ce473a8-1d21-76e6-1c28-99c2a5c59541"
   },
   "source": [
    "RMSE on Training set shows up weird here (not when I run it on my computer) for some reason.  \n",
    "Errors seem randomly distributed and randomly scattered around the centerline, so there is that at least. It means our model was able to capture most of the explanatory information."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_cell_guid": "a70803d8-638c-bdfa-6897-aed8ce78f475"
   },
   "source": [
    "**2* Linear Regression with Ridge regularization (L2 penalty)**\n",
    "\n",
    "From the *Python Machine Learning* book by Sebastian Raschka :  Regularization is a very useful method to handle collinearity, filter out noise from data, and eventually prevent overfitting. The concept behind regularization is to introduce additional information (bias) to penalize extreme parameter weights.  \n",
    "\n",
    "Ridge regression is an L2 penalized model where we simply add the squared sum of the weights to our cost function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "_cell_guid": "1fb3f0d6-a070-9ce5-7cc3-01a7e26faa4f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best alpha : 30.0\n",
      "Try again for more precision with alphas centered around 30.0\n",
      "Best alpha : 24.0\n",
      "Ridge RMSE on Training set : 0.115405723285\n",
      "Ridge RMSE on Test set : 0.116427213778\n"
     ]
    },
    {
     "data": {
      "image/png": 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Nn9GfHeTJdCz35+ei0RwMWrBo+oz+XESy7xzL0VFt/fm5aDQHgxYsmj6md01B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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e5a2610b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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2FSaXiw23TeC7xy6muKSG3ta6Nv2+tofPvaUE3vEQKCHGHwBCiAFSyh3G5uXA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e573609e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ridge picked 316 features and eliminated the other 3 features\n"
     ]
    },
    {
     "data": {
      "image/png": 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SLPi5wrVJorhtvylpa+AcSXOSHO32tu/N9c4lBYs9TnpJqMzWOztOEDSVhRYa\nwIXHblnqmXRvlvpcaKEBrTYhmEKEFnfJkLQL8Ctg9cK+9uQitLhbRJlth7C/1YT9rSW0uKdRbJ8F\nnNVqO4IgCILJSxyzCoIgCIJeSLdn0JK+BE62vX/+vi8wq+0jGrQZCixm+4QGddYA9rM9tMa1l4Hl\nbI/qps2HAmNsn9Kd9t3tV9KKwDBgRlKU9eW2j8j3+pntB5ppTx5zPPAk6SXsC2A32w82e5wgqCak\nPptPyHtOm/RkiXscsJGkYzvrMG3fwMTHhepRb2O82xvmORK7VYwANrH9TD4KpVz+PeAjoOkOGvjY\n9mAASesCx+XxJtAJ6dEg6DIh9dlcQt5z2qUnDvoL4BxgH+CQ4gVJ85L2SRfIRXvZfiDLXg6xvbuk\nAaRI41mA63OdyuGx2SVdCSwJPGJ7m1zeB/iNpB8CY4EtbY/MySXOB+YB3iFJcf4ny2B+CgwC7gPG\nAEtkec4FgGG2T8827wPsQHoJOM/2sA7KDwa2Bd4C/kP7ueRazJfrYbsNeD7bvAvwhaStSMez/tPg\nPj4kHaf6GnBAQdpzP5JgygzAtbYPLzyrCnMCo3L9NUgyoaNJLwqLNrA7CLpFSH0GQc/pyR50G+mM\n7laSqk9lDwNOsb0iSfDjvKp2lTqn2l6G5JiKs+NBpDPFiwMDJa1SuDba9tJ57GG57HTSGeVBwCX5\ne4X+tle2vV/+LmAdYEXgUEn9JC0HbAcsD6wM7CRpGUmDG5T/DFgaWD9fb8RpgCVdLemXkma0/Srp\nJeZU24Nt39fBfcxve1VgKHA8gKR1gO/YXoEkJzokZ74CmFnSY5KeI71IHVnoa1lgd9vhnIMgCHop\nPYritv2RpBHAniSN6QprA4vl5VyA2STNUtV8ZZKwBiRndGLh2kO23wCQ9ASwEHB/vnZZ/vNSoLLn\nuzLp3DLAhWQHlrmyatybcsrI9yS9RZqRrkqafX6ax7waWJ00C61V3jeXjwPGSWqYhML2kZIuIsmB\nbglsTtLHrqbRfVyX+3pOUmXtcF1gHUmPZVtnBb4D3EtK9lFZ4l4p97dkbveQ7dca2Vyh7HJ7Zba/\nrLaH1Gfz6ay8Z5Gy/n4qlN3+ZtCMY1bDgMeA4YWyPsCKtj8vVpRU/NpWVb/IuMLn8Uxs5yRiHh3w\ncdX3Rn0X7WkrfK4ub6OLaly2XwbOlvRn4B1Jc9Wo1uh+inb3Kfx5rO1zG/Vl+0FJ8+atB5j0mdSl\n5GcRS2tA9bmKAAAgAElEQVR/mW3vTcFVUwudkfcsUubfD0wd9jeDnjjoPgC2R2fpyx1pX8q+lTSr\nPglA0jKVdIkFHiQtf19BmlF2ls2AE3KbSnDVfcAWwEXA1sA9XbmHXH+4pOOAfqRZ7NakmfJwScfW\nKT+GtPc7lAZnkyX9yPbN+esipP3790l74nMUqt7fyfuo2H0LcISkS2x/LOkbpKjwdwt1kLRotvm9\nxo8jCJpDSFI2j3iW0y49cdDF2d7JwK6Fsj2BM7PMZD/gblJe4yJ7AxdJOojkaOqpYlXPmOfK/X5K\ncmaQ9quH54Cpd0hBXdVt6/Zt+3FJF5ASYbQB51ReKBqUXw48RQr+eqiDcbaRdAopsO0LUnBbm6Qb\ngKskbUAKEtsduKAT91Gx++/Z+T6QVyfGkBz7u8BMhaVvgG3zmB2YGgQ9I6Q+m0/Ie06btEzqU9LM\ntj/JnzcDNrf90w6aBVOWkPpsEWW2HcL+VhP2t5apQepzOUlnkGZ4o4Gft9CWIAiCIOhVtMxB52xM\ng1o1/uQgv3CsSnsQWRvprPWIlhoWBEEQlI4eOeiQ+5yk35G2d6tzfTiwBik4bCbgUttH1ql7J7Cv\n7ceqyn8O7EX7C8DBtm+QdDhwl+07qurXfY5BEARB76anM+iQ++wa+9m+RtIMwHOS/pIFSyYgqaZ4\njKT+wEHAoHz+fBaSQhm2D20wZuQTDaYoocXdPEKDe9qmpw465D47L/dZsZ18v23k88h5VeByksDL\nBMGWLPRyPvA6cC1J7nMsgO2xwKu53nDghuz81wNOzX3fV+hrFpIy2RLA9MBh+WUpCJpKaHE3h9Dg\nDnrqoCtyn09LOr7qWkXu835JC5COUi1eaFepc6rtKyTtzKRyn4sDbwL3SVrFdkVNbLTtpSVtk/sY\nSrtM5kWSdsjfK1Hh/W2vDBOWokVKHDEnSYLzj3m8iqxnP+Cfkv6RP9crr8h9zkASa+nIQZ8g6RBg\nIPCHfF65wru2h2QbdyE50YuBp20fm2fWbwMvS7oduMb2jcXOJc1IemH6Xn5pubxw+WDgdts7SpoT\neEjSbZVI+iBoJqHFHQQ9p8dBYiH32Tm5z8z+eZY7C3CHpBsLKSAvr6p7Nikt5bEAtr8E1pM0BFgL\nOEXS4Kr9/kVJ++Aj8/eLgJ3y53WBoZL2z99nAL4FuJHBZZfbK7P9ZbU9pD6bR3ckPiuU9fdToez2\nN4NmRXGH3GcXsD02z8JXIymq1bLxPmBNSafkl4BK20eARyTdRlr+rg7Iq2dTH2Bj2y92xdaSn0Us\nrf1ltr037N1OLXRV4rNCmX8/MHXY3wx66qBD7rOTcp/FsSRNR8qmNaxB3fNIUd9XSNoI+Copo9Xj\n+fqy5D3oAs8DC0paOGt/b1G4dgtJcW33bMMg2090YG8QdIuQp+w58QyDZuxBVwi5z445IQeWzQDc\nZvu6OjZWbDo17xf/BTgQOEnS1/N9v0PKJ12sPy7v5d8s6WPSS0dlvfFI4DRJT5FeFF4GNuiEzUHQ\nJULqs3mExOe0TcukPiHkPktASH22iDLbDmF/qwn7W8vUIPUJIfcZBEEQBDVpqYMOuc8gCIIgqE2r\nZ9C9DkljKmIpkn5EOsa1DvAj4ON8zno74Bbbb1a3r0h9FgVZmmTXhsDhpPPRXwCH2766m30tCNxo\ne6lm2BYEQRA0n3DQk9IGIGkt4DRgXduvk84lV9geeIYkotJhXz1F0jKkqPW1bb8maSHgNkkjC1Hd\nXSUkQIPJQkh9NoeQ+QzCQU9KH0nfJTnkH9p+BSYokH0EvAIMIUWff0ISSFma5MxnJUVYr5X76i/p\n/4ABwHW2f5P7Woc0G54BeIkkSzo2S36OIB3Zmg7Y1PYLwL7AMbZfA7D9Sj7etS+wdTG5hqR5SNKo\nC+eZ8oUkaVGA3QrCKEEwWQipz54TMp8BhIOuxYwk3evv1RD1aLN9taTdgH3y0azpScpmm2YHORvJ\nSQMsQ9pj/5wkKfqHfO0QYC3bn0g6gKRlflRu87bt5ST9CtgP+CVJP7uosgZJVrRm5izaZ8dvk2bd\nn0n6Nkl5bfmuPY4g6Doh9RkEPScc9KR8TpIU/QUptWM9KmH0Av5XSQ1p+yOYoJh2e+H7s8CCwFwk\njfH7sgzq9LRLmEJ6OQB4lHbp0u4yPXC2pEEkxbQuv46XXW6vzPaX1faQ+mwOPZH5hPL+fiqU3f5m\nEA56UsaTkmDcIem3FS3sDqh35q0oKfol6Xn3AW61vVUHbYoSpP8iLas/Xag3hPbkHF+QlM0g5Zqu\nsDfwZk4s0o+JtdI7RcnPIpbW/jLb3uq926mF7sp8Qrl/PzB12N8MwkFPSh/bn0paH7hb0pu2h1fV\nGQPMkT8bmF/ScrYfzUvcjRzhg8AZkgbafiknzujfgUb2SSTJzztsv5qDxPYgyaRC+774I8CmhXZz\nklJVQkqLWYw4acpB+iCoRchU9ox4fgGEg65FRTZzdM45fZekd5g46vkC4CxJY0lBYpuTnO7MpHzN\nazfo911J2wOX5vSQbaQ96RepE1lt+0lJvwFuyG0WBNa0/e9cpeLAdwJuKjT9I3C1pG2BvzFxQo6I\n4g4mCyH12RxC5jNoqdRn0D1yBPeKwA9y2szJRUh9togy2w5hf6sJ+1vL1CL1GXQD2we12oYgCIJg\n8tK34ypBEARBEExpwkEHQRAEQS+kJUvcksYDT9KeTOIy2yc0qN/Z407V7c4BTrH9fBfa7Eo6/zwA\nmM/2qAZ1FwRWsX1pgzprAH8FRpKiqN8CtrT9bo26NfW7s4rZTiThEYC/xTJ30FsJqc/uEdKeQTWt\n2oP+2PbgLtQ/COiSg5bU1/Yvu9oGuBe4AfhHJ5osDGxJUuhqxN22N8hjHAPsSpL6LI5d+T+zXtTe\nKbZP6YRNQdBSQuqz64S0Z1CLVjnoSSLcJM0BPAQMtf2ipEuA24FvAzNLegx41vY2krYinQOeHvgn\n8GvbbZLGkDS01wJ2k3QU7RrVWwC/zcPdbPvAPG6xza6278/lE9koaXVgGMmBtgGrk14aFs22jbA9\nrNH95j5nJyfZyDPjgaTZ+qvArYXx1ie9mAxt8Mx+B/wYmBm43/YuuXwgcBYwH0nEZFPbL0vajyTC\nMgNwre3Dq/sMgmYQUp9B0HNatQc9s6THJD2e/9zU9oekmeUISZsBX7F9nu3fAmNtD87OeVFgM9LS\n8mCSQldFlWtW4AHby9q+rzKYpK8DxwHfI2ljLy9pgxptipKb1exHehEYDHyXJEZyIHBPtq2ecwb4\nbnbir5JeBM4vXFsM+H5RWSynljyAlKyjssS+d35Wj+VkGwCn217R9tLALNmpA1ycrw0CVgHeyG2+\nY3sFYFlgiKTVGtgcBEEQtJBWzaDH1lritn27pJ8BZwL1chWvBQwGHs4z0ploT/s4HrimRpvlgTsr\nzk7SxaQZ8PUN2lRzH3BqbnuN7f9mve3OUFzi3p+U+OJX+dr1tj+rur8hpDSXxU2wWkvca+X+ZiFp\nfD8j6S7gG7avB6j0LWldYJ38otCH9GLyHdKSfl3KrodbZvvLantocXePnmpvV1PW30+FstvfDHrV\nOejscBcjKV7NA7yRLxWXd/uQlpMPrtHFJ7br7eHWOzher81EZbaPl3QjsD4p0cW6dfrriBuAqwrf\nP666/hJpb1ukhBk1yYpiZwKDbf8vL5dXdLhr3Wsf4Fjb53bF2JKLBZTW/jLbPmrURyFV2UXGfvB2\nj7S3qynz7wemDvubQa/Zg87sQ0oM8VtguKSVbI8HPpPUL3++HbhO0mm235E0FzCb7dcb9PsQMEzS\n3MAHwBak/eRGtvQpXpM0wPazwLOSlgcWBf5DuyZ3Z+/3uyQnXI9XSMvp10raxPZzderNRHqJeC/r\nf28CXGn7I0mvS/qJ7b9KmoEUPX4LcISkS2x/LOkbwOe23+mE/UHQaULqs3uEtGdQTasc9EyFpdY2\nkk70BcDPgeVtj81LtYeQop3PBZ6W9Gjeh/4dcGuOuv6MtHf9OpNGQFf0r9+UdCDtkdk32b6xWKeC\npN1J+79fA56UdHOOBt9L0pqkJfFngf/LbcdLehy4oME+9Gr5fvsC75NSWdbF9gs5EO5KSUPr1PlA\n0rnZljdILyEVtiWlmTyC9Hw2tf33vH//QF6aHwNsDYSDDppKv379WGSRRUo/Ayqz/cHUQWhxB40I\nLe4WUWbbIexvNWF/a2mWFncoiQVBEARBL6RXBYmVmRw0djztS+Z9gJG2N26dVUEQBEFZmWIOWtJX\ngVNJaRJHk/ZGT7D91yllQ7Zje2DP/HVx4HnSvnKP5DNt30pBaKTO2IsCp5DEScYALwB71JL9rNO+\nH+m5PUkSaXkG2N72uE627wMcYPv4ztQPWsf48eN56aUXW21Gt5l77mVabUIQlJ4pOYO+DhheEeSQ\ntACwQeMmiUIEd4+xfQEpIA1JI4Hv2R7djL4bIWlm4EaSWtktuWxN0nGyDh10QQr0g8oZckmXkTS6\nz+ikGdOTxFXCQfdyXnrppdLKZY794G0uPHY25prr6602JQhKzRRx0JK+D4wrnsHNx6LOzAknLiSJ\nbQDsZvvBnGTiSNJsWyRJzWuBb5KOGA2z/efc/46kyOvRwFPAp7b3kDQvSfJygdz33lVqYROOUuXZ\n5QukKPL3c4T4i8BywOmkGe8KwGzAXrb/lp3mCcCq2aY/2C6qhBXZGvhHxTnnZ3BnHnsA6aVhVpIy\n2q9tPyxpLVIk+0ckOdClmfjI1j0ksREkHQBsQ1piP8f2GVny83rgcZKC2kPA7Dmi/Cnb29exNegF\nhFxmEEzbTKkgsSWAx+pcewtY2/YQYHOSM6ywLLC77UXz9x1sL09SBttT0lxZxvMQkvNclXQ+ucIw\nkgLXiqRzwn+uZ2AWK7mEdtnQHwAP2X4/f/9mtnED4BxJ0wO/BN6yvVIefzdJ36wzxJLUFx75X34G\ny5EcefEZLAfsYnuJYoM8/nqk42crkM52L0eS9vy1pEp9ASfbXpI02/4wS5NuX+9ZBEEQBK2nVekm\nzwBWA8YB65Bm0suQ9oKL6Vwesv1a4fteWaca0kz6O8DXSTPTD3LfVxb6WBtYrJD4YjZJs9geW8e0\n84ErSApdPyedv65wBUw4o/xaHmNd0sx+i1xnjlz+n849iQnMBJyRn8EXpNlyhQds/7fwvTIDhnSu\n+wLSnvrVWdbzM0nXkQRR/g68ZPvxLtozgbLL7ZXV/tGj3+i4Ui+nrM++QtjfWspufzOYUg76WWBC\nNLPt3bKq16PA3sAbWYCkHykJRYUJMph5yfv7wIq2x0m6k8bSlpXyFW1/3hkjbb8qabSk7wGDcuBX\nheKB8YrASh/ScvSdnej+WVKAXC32BV6zvXWeGRcPAFZLgX5YrWPegSZ4dfsunc8r+VnEUttfdsr8\n7Mv+2wn7W0uppD5t3yHpaEk72z47F89GcnJz0D7j3JYkS1mLOYHR2TkvCqyUyx8mJbGYk+SMNibt\nQ0OKqt4TOAlA0jK2n+zA3PNJ2aDOqyrfFLhY0iKk2fuLJPnMXSXdbXt8vvZqnajqC4EDJK1bcfz5\nReDN/Az+nettT2MnWuvaPcBZkk4kBYL9hJRWcqL62cY2pVzZXzYYI+gFlFXPuqx2B0FvY0oucW8I\nnJaDmd4hOdMDgCeAqyVtS5L8rJ7xVfgbsIukZwEDDwDkRBHHkAKgRpGOTX2Q2+xJWj5/kuT47wZ+\nXeizlozatSTnPKKq/L+SHiEFcu1k+wtJZwPfAp6Q1Aa8TXKOkzho259I+nF+BqcDn+d735O0pH6V\npJ8DN9Vq38jmHFB2KfBIvn6m7WdzkFh1/fNI+9YPxz5072XgwIEM279Thxx6JQMHDmTUqHo7SUEQ\ndIapQupT0qw5AUQ/soPt7vlqSSsBR9teq1B2ISkRxfXNsbg0hNRniyiz7RD2t5qwv7U0S+pzalES\nO0zS2sCMwK09cM4HkSKdN6u6VP63mCAIgqBUTBUz6N5EjsS+gIklPz+2vVrLjOo+MYNuEWW2HcL+\nVhP2t5bSzKAljSdJU1Yiny+zfUKD+r+1fWw3xjmHdOb5+S602RXYi3SsaT7boxrUXRBYxfalDeo8\nRpLeXDYvt78P7Gz7knz9EeAXtp+oavcysFz1+HlPei/aI8YPtn1DDbtutL1UZ+876J2MHz+eV14Z\nCcDo0VM+H3EzCanPIOg5U2KJ++PqY0EdcBDQJQedo5J/2dU2wL3ADbTniW7EwsCWQF0HnftbhRRF\nvgwpmG0V4BJJs5BeBGpFkU+yjCGpP+lZDLL9UW4/X51xYxlkKuCVV0aWVt6zSEh9BkFzmBIOepKp\nvqQ5SFHXQ22/KOkS4Hbg28DMeSb6bD4bvRWwB+n40D9J547bJI0BzgbWIil4HQXsa/uxLBzy2zzc\nzbYPzOMW2+xakf0sCJlU7FudpELWlv9bnfTSsGi2bYTtYTXu9QHghyR50VXyn9vnaysAj2bb5yY5\n+m8AD9Z6RsBXgQ+BsQBZXOXVbN9ypGjsNpIYScXu7UhKZ5WXgets/yZfqymHWmPcoIWEvGcQBBWm\nhNTnzJIek/R4/nNT2x8CuwIjJG0GfMX2ebZ/C4zNUpTb5PPOm5GWlgeTdKorUpyzklS2lrV9X2Ww\nLP15HPA9kv708pI2qNGmqMldzX6kF4HBJEWuT0hJJu7JttVyzgD3kRwz+c+7gXGSZs3fK2Memvta\nihR1/q0afT1JOrb1sqTz8xGtCueTXjCWrdFuGdKZ7aWBzST170AONQiCIOiFTIkZ9NhaS9y2b5f0\nM9IZ4Hr7p2sBg4GH8yx3JpKwByRZ0GtqtFkeuLOynyvpYtIM+PoGbaq5jyR+cjFwje3/dqDWVbmn\n1yTNIOlrgLIs6MMkUZVVgD/kqqsDP81tbpY0STatLCSynqQh+TmcImkwaWY/Z+Gl5EKSJneF221/\nlO/9WWBB0tJ4PTnUhpRdbq9M9o8ePVurTWgqZXr2tQj7W0vZ7W8GLTtmlR3uYiRhknmAivhwcbm3\nD2k5+eAaXXySE1zUol4EXb02E5XZPl7SjcD6wH2S1q3TXy3uJ81gK/fzT9KsdXmyuEr1eA3sxfYj\nwCOSbiPNnIc1qs/EIidf0v533K2owpJHUpbK/jIHhdWiTM++mrL9dqoJ+1tLmaQ+6zmGfYB/kfaK\nh0taKed8/kzt+Z9vB66TdJrtdyTNBcyWU1XW6/chYFje5/2AlOWpsiTdSLN7wjVJA2w/CzwraXnS\nkvB/SJKcHfEAKfJ6eOH7icCbtiu/uLtJS/VHS/oh8JXqTvKy9PyFRBfLkmREP8h64avkZfqtO2FT\nIznUoBcxNchkTg33EAS9gSnhoGfKgVWVY1Z/I50T/jkp9/JYSXeR9kgPJ2WQelrSo3kf+nfArTnq\n+jPS3vXrTDoLbQOw/aakA2mPzL7J9o3FOhUk7U4KnPoa8KSkm3M0+F6S1iQtiT8L/F9uO17S48AF\nHexDn0K7FOmb2fb7CnWOAC6VtDlpxv3aJL2koLiTsqP+lCSPuku+9nPgfElfkvTG61F5Jo3kUINe\nwkILDZgg7zn33OU+ZhVSn0HQc0KoZBqhm3KoIVTSIspsO4T9rSbsby3NEiqZElHcQe/gsDz7fxoY\n2V051CAIgmDKMLVocU9RctDY8Uws5znS9sb1W7UW2/u32oYgCIKg83TooPM+58mVf+Al7QvMavuI\nBm2GAot1IOm5BrCf7aE1rtWUvuwskg4Fxtg+pTvtO9nvJHu/ki4A1gYWtv25pHmAR2wvLOka0t71\n9bnu88BfbB+Tv18FXGT7uvz9NGAT299s5j0EU46idGdXCanPIAg6M4MeB2wk6djOOsysF31DhxXr\nS1R2e2M877G2ijbgC1IQ19mFMmgXMbk+R5h/DKxcaLsyOVd1PoK2IfCapDVs3zUFbA+azNQi3dlV\nQuozCJpDZxz0F8A5pGNRhxQvSJqXJGe5QC7ay/YDWXJyiO3dJQ0ALibJT16f61QOic2eRTOWJM00\nt8nlfYDf5CNIY4EtbY/MiSHOJ52bfgfYwfZ/JA0nRToPIjnCMcASku7Mtg2zfXq2eR9gB5LjPK8S\njd2g/GBgW+At0lGrRzp4XqcBe0s6t6r8fqCyorAK6QVmvTzGQiRBl8r5lO8BzwCXk/S/78r1DiVp\ngg/I97UPSQTlh9m2obbHZ0GTU0jKae+SEni8JWkPYGfgc+Bftrfs4F6CHhLSnUEQdJfOBIm1kdS+\ntpJUffp6GCmD1IrAJiR96GK7Sp1TbS9DciLF2fEgks724sBASasUro22vXQeu3Kk6XRguO1BwCX5\ne4X+tle2vV/+LmAdYEXgUEn9sob1diTRkJWBnSQtkx1avfKfkWQz18/XO+I1UtKMbarKHyW9NExH\nu+yns5xpUQYU0tntS4DrgB9VrQoMIDnwnwAXkZTDlia9oKyf+z8d2Nj28qTz2Mfktr8hJd8YRPuR\nrSAIgqAX0qkgsZxNaQSwJ0mXusLawGKFZBOz5axLRVYmORNITufEwrWHbL8BIOkJYCHaHdVl+c9L\nSbPBSl8/zZ8vJAVqVbiyatybbH8BvCfpLdJZ51WBa21/mse8miS72adOed9cPo6kqX19jcdTi+NI\nzvXm3De2P8vSm8uRZr3HAwOzTcuSz0lLmh74EbB3Phb1EPCD3BfA/9n+UtLTQF/blb3wp0nPT6QV\nib/nv5e+wP9ynSdJmbWuy/Z1SNnl9lpp/9Qm3dlV4rfTWsL+8tOVKO5hwGO0K2RBcj4r2v68WLFK\nt7qtqn6Roizl+Cp72up8rsfHXei7aE8xEru6vI1uSGTa/nd+4fgZE9t+H8nxz5YVwR4EdiOtJJyV\n6/wAmJMk1tIHmJm0zF9x0OPyGG2Sis+9IuvZB3jG9qo1TFs/j78BcLCkJbPmd11KfhaxpfaXOcir\nGcRvp3WE/a1lSkp9VmaAoyVdAexI+1L2raRZ9UkAkpaxXZ3v+EHS8vcVwOZdsG0z0p7t5rRrWN9H\nWv69iCRxeU8n+6o42XtIsqLHAf1Is/GtSbPM4ZKOrVN+DDADMJR2R9oRxwA3MbGDfgA4Gbgzf3+K\nNJv+qu1nctkWwI62rwDIKxIjJc3U4L6KGJgvS6c+mJe8F7H9L+Bbtu+SdD/p+c5GSmkZTCamRdnL\nafGeg2By0BkHXXQwJ5OkNitlewJnSnqS5NjuJkciF9gbuEjSQcAt1JeYrJ4xz5X7/ZTktCDtVw+X\ntB85SKxG27p92348H4V6OJedU3mhaFB+OcmRvkWSyuxwnDzWv7LE6aDC9ftJQV5H5zrjJb1Ne57n\nmUkz6J0L/YyVdC/p5aCmvGmRfLxrE+D0rL3dDzhN0gukv4c5SI59WE77GUwmitKdXSWkPoMgmOxS\nn5Jmtv1J/rwZsLntn3bQLOgdhNRniyiz7RD2t5qwv7U0S+pzSiiJLSfpDNKsbTTpjHAQBEEQBA2Y\n7A7a9r1MvMxbevILx6q0B5G1kZaMR7TUsCAIgmCqoSkOelqTA7W9W3f7zXvdm5ICwz7OZaeR9tfn\ntT1K0r22V8vCLKvYvrSDe+nSs2j0XIPm0BOZTwipzyAImjeDDjnQztMGvEg6G35JPkq1JknEBQDb\nq+WPC5OUxBo6aLr3LCLP6GRkWpX5hJD6DIJm0SwHHXKgXZMDvYx0zOkSkirYfWTZz9zfmHz/xwKL\n5mjwESSFsBNIkd7jgXNtn5mfxR55VWI6YFPbL+QjWqcDSwDTA4flF6NgChAyn0EQ9IRm5YMOOdCu\nyYG+SDqr/BXSEbLqGXLl/g8E7rE9OL8M/BL4FrB0vr+LC23etr0c6WWocn8Hk6RAVwK+D5yUj3IF\nQRAEvZymBYmFHGiX5EDbgGtIIiwrkM49dyYsf23gT7Yr57rfL1y7Nv/5KO33vy4wVFIlF/QMJAff\nacout9cq+6d1mU+I306rCfvLT7OjuEMOtPNcQXKmw7NsZze6mIjKvRTvow8pacaLxYqS5u9spyU/\ni9gy+8sc4NUs4rfTOsL+1jIlpT47Q8iBdlEO1PZrWV3ttga2jAGKf9N/B3aW9I+sQjaX7dENhrmF\ntD2wO4CkQbaf6Mi2oDlMq5KX0+p9B0GzaZaDDjnQ7smBnlurvPD5KeBLSY8DF5D20xcBnpL0GXAu\n8McG93YkSebzKZLTf5mUKCOYzPRE5hNC6jMIgikg9dkZQg601xJSny2izLZD2N9qwv7WUiapz84Q\ncqBBEARBUKBXOOiQAw2CIAiCiWnWOegJSPpS0omF7/tK+n0HbYZKOqCDOmtIqimyIellSXN3z+Ik\nz5lFSJpGlgO9DrjI9rL5LPMkzlnSPpKek/SkpMclnVRROpN0Y04PiaQx+c+6z6GzSNquK5HcQRAE\nwZRncsygQ/az82PvQjrbvILtMZKmI6mxzQx8ZPvHhepdPVJWb8y+wPbAM8Cb3e0naExocYcWdxD0\nlMnhoEP2s/OynwcBq9keA5BFUyYkD2mQBGNOSTcC3wbusP3rXH8d4HDSca+X8v2Ozf1cTnoZOBUY\nQoqa/wRYOYusBE0ktLhDizsIesrkcNAV2c+nJR1fda0i+3m/pAVIR6oWL7Sr1DnV9hWSdmZS2c/F\nSTO/+yStYruiKjba9tKStsl9DKVd9vMiSTvk75Xo8P62V4YJGahE0sWeE7CkP+bxKvKe/YB/SvpH\n/lyvvCL7OQNJtKWmg86SqLPafq2DZ1mL5YHFgNeAWyRtBNxFeiFay/YnectgH+Co3OZd20Py2DsC\n+9p+vMHYQQ8JLe4gCHrCZAkSC9nPLsl+kvtYN9v3FWAL2w9SX6HsIduv5naXAquRthYWJ7249CEl\nx7i/0Obywuc+DfqeiLLL7YXUZ+uI305rCfvLz+SM4g7ZzwbkPeePJC1o+1XbtwK35gCwGTpoXn1/\nlXFvtb1VnTbV99spSn4WMaQ+W0j8dlpH2N9aepvUZ5GQ/ey87OdxwJ8kbWH7gzzznakDmwBWzPvr\nr98ECnoAABnkSURBVOf7Ppv03M6QNND2S3llon+1DnfmQ2COxo8g6CnTquTltHrfQdBsJtcedIWQ\n/WyA7T9JmpW0h/0p8BHppaKyN1xvVeAh4Azag8SuzWNvD1wqacZc/xBSasvq+x0BnCVpLBEkNlkI\nqc+Q+gyCntIrpD6LhOxnryKkPltEmW2HsL/VhP2tZWqT+iwSsp9BEATBNE+vc9Ah+xkEQRAEvdBB\nT41k2c8gCIIg6DS92kFL+hpwGkn56n1S4NVetv/dgz7XAPazPVTSUGAx2ydI+glg28/neocDd9m+\noxtjiHS8bDBwkO1TOmiCpA2Ba4BFbb9Qp86cJJW0P3XVpqB59FTGszOE1GcQBL3aQQPXkpTAtgCQ\ntBRJQKTbDjpTidIuaoBvCNwIPJ+vHdqD/t8Dds99dpbNSce6tiDJdU5E1gyfixT13iUHLamP7d4V\nDVhipmUZz84QUp9B0Bx6rYOWtCbwme1zK2W2n87XTgTWA74Ejs6yoGsAhwHvUqXVLWk9kgb1x6Rj\nTJUxtiPNzi8BNgBWz1raGwO/B26wfY2ktUiKZv1IR6t+ZfvzrHE9gnTeeTpgU9sv2H4XeFdSMdlF\no3udlbRHvSbpJeHwXL4GcCQpWE6k41cDJT0G/N32b/IRsp+Rzl1fa/vwfEb6FuCfpFn8FZLmtr13\n7vcXpJWDfTtjXzApIeMZBMHkpunpJpvIksCj1YVZd3pp20sB6wAn5qVwSMFle5AkLwdKWiWfCT4H\nWD9rUVenWWyz/QApMcf+OS3ky4XxZiQtV29qexmShOavCu3ftr0cSZBk/27e60+Av+Wl+3clLVu4\ntiywu+1FgQOBf2cbf5OTY3zH9gq53hBJq+V23wbOyM/pFODHhcxdO5CSiARBEAS9lF47g27AaiS9\nbWy/nZNULE/KSFVLq/tjYKTtyqbhRcBOXRhPuf1L+fsI0jLzH/L3a/Ofj9Ku+91VtiDttUPSzN6S\ndrGShxok1FgXWCfPqPsAswLfISmMvWr7YQDbH0u6g+Sknwem8/+3d97hclXlGv9BUHqzIL3DK733\nIhfkXkGKgArIpYgCSkeqoHLFS1VEDEVRghQNIIIihEe6hBKBUEN5L2joGEVAgwIGkvvHWjtnn8k5\nM3Omnkm+3/PwMLP3Xmu9s2dOvr3a+9lP1COs1/1w26E/fLbrI3473SX09z7DOUA/QbL8rEV5Q/hg\nftrNbhqvVr5oczD/7qpIWhjYGlhd0jTSMPo0+nrj1Ty0ZwNOL08D5DqXGaDcxaT0lk/T3x+9Kj1u\nFtAW/a+//lbYWVahuDfx2+keob+7DGcv7pZg+3ZJp0r6su2fwvRFYm8Cu0u6jJTneQvgGFL6xYF4\nGlhG0nJ56HrPQa6bzMD+1M7ll8+98L2BO4fwUWo9HHwOuMz29GFzSXeUhqorNZa/+d8Bp0j6Re4l\nLw4UiUj6tWv7/pzicx1SOsygQZq18ayHsPoMgmDYBujMLsC5kk4gpa18DjiSNJT7KGmR2LF5qLsy\nQBcrtd/NeaXHSPonaaX0QGOUVwI/kXQYqedeLv9F4Jo8h/sAKTnF9DYqyXPiD5KC6VRJRwCr2h7o\nX9zd6Z8GE+BXpAeJq8sHbb8u6R5JjwE35XnoVYD7ckawyaSkHVMH0XY1sJbtwfzNgzoYMWIEK6yw\nUlvb6PUexIgRI2pfFARBVYadF3fQPnIqy+/bvqPOIuHF3SV6WTuE/m4T+rvLzOzFHbSYbHByP/Dw\nEIJzEARB0EUiQHcISR8CbqNv6Lnw5N7G9hvtbDsPaaudbQRBEAStpaEAnc089iStXH4fOKjY0jPA\ntZeQDT9q1HkM8CXSXPMUYKTtKxrRV1HvRGC9PH97t+3N8yrnTW2PztesB+xt+8hm26tou9K+c52y\n1Wgr2xqirjuAo20/1C0NvUxYfdYmrD6DoHka2Ra0MbA9sLbt93LP8IPNiJD0FWAbYP28Gnk+Gt9T\nXMn0SXbbxcro5Uh7jYv91OMZwBSlBQxm39nyiX9JI2y/3+p6gxkJq8/qhNVnELSGRnrQiwGv2X4P\n0spiAEnfBHYA5gbutf2VyoKS1iW5Ws1LsuTcz/Yk4OvAlrb/met8C7g8lxmSzWZ+YBgNLA6Mo7Td\nSNJk2/MDpwMfzwYflwKP0JdAY2GSy9bypL3EB9qeIOlkYOl8fClSusiRg92kwew7MwtKuoHk9nW7\n7YMLfcC5+T7+C9jZ9l9zj38UaVvZX4Ev2n4pj068Q3JQuyeXX66k8WvAxsB2wEvAjhHEW0NYfQZB\n0G4asfq8GVha0tOSzpe0ZT4+0vZGttcE5pH06XIhSXMAI4HdbG9AMss4TdL8wHy2n69saIg2m8fk\nYycDY7PF5XWkoFpQ9FxPyNesa/vcinPfBh7K7Z1EflAoJJHsRTcCTi5ZZw5ENfvODYBDSHu3V8z2\npZAeXO61vTap5104no0kJQ1Zm+QbXn4wWML2JraLz788sFVu/wrgtvydvAP0+06CIAiC4cuQe9B5\nCHpdkkHI1sCVeZ/yW5KOA+YhZV2aANxYKiqSv/YtkmYjPRy8ks8NtiS9EZvNLYvXtsdIGuoCrM2B\nXXP5OyR9KA+5A9yYRw7+JmkSKbPWK4PUU8u+83kASaNzm9eSkoOMKX2mT+bXm5Q+3+X03zf9y4p2\nb7I9VdLjwOy2b87HHydZnw6JXrfbC6vP7hG/ne4S+nufhhaJ5dSFdwF35UBwELAGaTHWK3k4eK6K\nYrMBE2xvVlmfpMmSlrX93ADNNWuz2ZL9aBXtQTIDGbDNOuw7K+egi/dTSsfKn6nanHWlpee7kL4j\nSeX6BtVbjR7fi9g2q8+gNvHb6R6hv7t0zepT0srA1Dx0C2n+82lSgH499zY/y4w9OwMflbSx7XF5\nyHtl208CZwDnS9rD9uQ8f7sryflqqDabdwF7AadK2g5YqHSuCNaVlpllxpLcuP5X0lak+fa3slNX\nvdSy79wozyu/SHIS+1GN+u4l9civyNrG1qmjlQ8nQYnw4h6cuDdB0Boa6UHPB4zM5hfvAc8CBwJ/\nJw1rv0oyxSgoLDOnSPpsqewI0hDwk7YvzIH9AUn/JvUkz27EZpM0hzxa0h6kwFbOBFWUeYxkwfkw\n8DPSIrGC/wFGSXqU1DvdZ5B2qvVqq9l3XkW6P+fRt0js1zXqPBy4JG9F+yspXWQtDdXOh31cE4QX\nd23CizsImiesPoNqhNVnl+hl7RD6u03o7y6tsvpsZBV3EARBEARtJqw+m6Cb9p1BEATBzE1TAVrS\nVNJc8bH5/dHAvLZPqVJmR2AV22dVuWZQO8yydWeDmk8GJtv+fiPly2QN69RTb9nyVNKdwKKkvckf\nBG4FvlmkgZS0BHA+sCop6N8AHEcyPSnmtlcEXiYZmjxG2i/+G+BPpBX0N5a+l31JZi8v5XMX2S62\ngAWD0AlLz8EIq88gCJrtQb8L7Crp9HoDpu3fAr+t49KWL3CqYSzSSaYBe9p+OK9mP4MUXLfK568F\nzrf9mbxn/CfAqbaPIxnFIOl2kp/2w/n9J4C7bO8kaS7gYUnX2r4v13ml7cNzr9+Sfmn75Q593p4k\nLD0bI6w+g6A1NBug3wMuIllKfqN8QtJHSNuHlsqHjrR9X+7NrW/7MEnLAz8nmZtcn68ptj/NL+mX\nJHOTB23vnY/PBhyft1D9C/iC7T/Va4dJ2mK1Wk4Y0c+yU9LXSCukpwEXFy5jVY6fRFrlPYnUO31w\nCPduNoDsZ34c8IykNYCPAm/bviyfnybpKGCipG/ZfqdUfsCFCLbfkfQIMIMXZU4a8izJsjUCdA3C\n0jMIgm7R7CKxaaSh2L2yZWeZc4Hv296ItC/64opyxTXnZFvNl+jfO16btL1oVWAFSZuWzr2R7SvP\nz3XA0OwwZ7DszBmt9iXZcG4CHCBpreyaNtjxzwNrkiw0N6jjfg2I7amkYeqPA6tRkbjD9mTgedKw\ndk2yUcqKpD3hleeWBubM7QVBEATDlKYXiWUTj0uBI0ipIgs+CaySh2gB5pM0T0XxTUie0ZCC6ndL\n5+63/SpA7g0uS9rXDHBl/v9oUvKNoq567TAHsuzcDLiu6KFK+hXJNnS2QY7Pno+/C7wr6foBbs9Q\nqLUsv55l+1vmvd0rAT+wXXaM2CMPgws41Pa/6xHV63Z7zegPS8/mmJV/O8OB0N/7tGoV97nAQ6SF\nSgWzARvZLttNUuHINa3i+jJlW81KK89pg7wejAHtMAepu6ynvDq78vg0WuTUJWl2khPbU8DrpBGH\n8vkFSMPxz85Yuh/FHPSywDhJV9suesrFHPR6wM2Srq8I4APS43sRm9Lfy4u0hgOz8m+n24T+7tI1\nq88KinnUNyRdDXyJvqHsm0m96u8BSFrL9qMV5ceRgtHVpNzJ9bI7cFYuUyyCuofm7DDHkty6ziC5\nnO2S65k9Hz99kOOnkVZi70hty84Z2s2LxE4DXrA9AZgg6XRJ/237iryw7Xuk4ft3qtQ3HdvPZb0n\nkJJ0lM+Nl3QZcCRw4hD0zpKEbeXQiXsWBK2h2QBd7r2eTUqhWBw7guSv/SgpsN1FykRV5ijgCkkn\nAr8j2YXWamcasHCu9x1SUIYm7TDziuqfkexEp5G2Ij0KUOX4VaS53En0tzet9Rkgfe53SfPBt9I3\n1A/pIeBCSd8iBfIxpNSX1eqr5MfAMXnOuZKzgPGSTi1ycAcz0glLz8EIq88gCLpq9Slpbttv59e7\nA3vY3qVGsaBzhNVnl+hl7RD6u03o7y6tsvrstpPYepLOI/US3wD277KeIAiCIBgWdDVA276btJ1q\npiE/cGxG3yKyaaS91pd2VVgQBEHQUwwpQM/q1p711Gv70Hz+EuATwJvAkZIOsL35APU09fnq0LkM\ncIPtNdpRf6/QTdvORgirzyAIhtqDDmvPoXG07etqXNPSRQCSZs/GJ21roxcJ287OEVafQdAahhqg\nw9pzaNaeMzi1ZS/s0cDipG1mxXarY4B3bJ8n6RxgTdvbSPoPYH/be0u6AFgfmBu4xva3c9mJwFUk\nc5izspXnqKz/llLbq5L2qn8ga9vN9h9rfIaZhrDtDIKglxiq1WdYew7N2vO7kh6S9LCky/Oxk4Gx\necj5OqDYBjUW2CK/Xg+YN48AbEGfZeeJtjcE1gK2krR6qa3XbK9v+2pSED7E9joVer5CchhblxTo\nX6rjMwRBEARdYMiLxMLac0jWnsfYvrbi2JaFbttjJBV5o8eTVrXPT5pKGE96CNgCOCxfs4ekA0jf\n26Kkh5kJ+dxVWe+CwIK27yndm0/l1/cBJ0laMn+WWs5kPW+3V+gP287OM7P8dnqV0N/7NLqKO6w9\nG6dSfzmr1XPAfqSh+cdI+Z9XsP10tu88mrSg7B95KH+uUj01DUdsj5Y0DtgBGCPpQNt3VivT43sR\np+vv5QVXvcrM8tvpRUJ/d+mW1WdYew7N2nOggH4XsBdwap5XX6h0bixwDGn+ewJwDn3z3AsAbwGT\nJX0M2A64o7Jy23+X9KakTW3fm7UDIGk52xOBkdlhbE3gzhqfYaYhLCg7Q9znIGgNQw3QYe1Zv7Un\npAVbJ9HXC98QOAUYLWkP0hD+C6Xrx5L8se+z/bakt8nzz7Yfy0P/TwEvAndXfqYS+wOj8ra4m0vH\nPy9pb2AK8Cpwah2fYaagm7adjRBWn0EQdNTqM6w9e46w+uwSvawdQn+3Cf3dpVetPsPaMwiCIAjq\noKMBOqw9gyAIgqA+up0sY8jkedUrbO+T348A/kyat91J0iKkhWtLkQw5JtreQdLBwAH0zdd+AFiN\nZEPqBnTcQDJNObTpD9VX54akrWeLkExZxgOHV+aBlrQ2aZ/zAVXqmm6fms1i1rN9uKRDgH/ZvmSw\nskNluNpo9rJdZi9rh7D6DIJW0HMBmrSdaHVJc+Y9yduSFk0VnALcXHILWx3A9gXABcVFkk4FHmok\nOOf6dmhQ/4DkB4urgc/bvj8f2xWYn7Q4rsyJwHfqqHagBQajSCvgWxagw0YzKBNWn0HQGnoxQAOM\nIbl5XUta1T2aPheuxUgrxAGwPaGysKQtgc8B6+b3cwIXkty1ppA8tO/MPc+dSNakywO/tn18LjOR\n5Pg1P3ATaVX1piR3rp1tvytpA+CnpL3XtwLbVUlacQjwsyI4Z+2VJidImg9Yw/bj+f0GpH3pc5KM\nY75o+5nBblxeHT5R0vq2a1mV1k3YaAZBELSWoVp9DgemkZzF9syBdU3gD6Xz55O2GN0m6URJ/R7j\nJS1E6j3uY7sYQzwEmJrtRL8AXCrpg/ncWqRgviawu6QiCpV7pysCI22vTto6tls+Pgo4IFtrvk/1\nLWCrk4a0a7E+fe5hkLZdbW57PZKN6Ol11DGevgeaIAiCYBjSkz1o2xOys9aewI2UDEFs3yxpOZK9\n5fbAQ5JWt/23fMmFwKW2x5Wq3Bz4YS7v7Oi1cj53WxHIJT0JLAO8TH8TkolFj5YU/JbNlpvzlXrE\nvyD1+ptlMdK+74KFgMskrUR6AKjnO/0LyZ+8JvU44oSNZjAQvW7VGPq7S6/rbwU9GaAz15MWVG0F\nfKR8wvabpF72lZJ+S/K/vi4PWS9NcvKqRjn41mMTWnlNYcE5lL1wT5B6x7VSc75Nf4vP7wC32941\nZ/iawV1sAOaiv4/6oNSzF7GXFzMF7aPH97GG/i4yM+hvBb0YoIugN4qU5eqJvGIZgJyecVyea50f\nWAF4Iae6PJU0HFyZL3ksKWjfKWll0gpwk+aYh6JpOtly8x+SNrD9ALWtTc8D/iDphnw9knYB7rZd\n7jE/RfLkLliA1KOHPje1WqxMfyeypgl7x6AgfgtB0Bp6MUAXVp0vk4JaJesB50maQppjv8j2eEk/\nIuVRvjYn8Cj2LB9GWt19oaTHSIvE9rU9pSLRx/S2a7wu82Xgp5LeB37P4Nam2P5Ltv88W9JHgakk\nm8+bKq6zpAUkzWv7n6RRhEslfYM03F8Pm5Hmq1vCcLXR7GW7zF7WDmH1GQStoKNWn7MapSCKpOOB\nRW0f1YJ6jwAm2x7VQNm1gaNs71vH5WH12SV6WTuE/m4T+rtLr1p9zmp8WtLXSff5OVIqyVbwI1JW\nsEb4MPDNFukIgiAI2kT0oDuMpP8EzqR/7uk/2d5t8FJBEATBrEYE6CAIgiAYhvSiUUkQBEEQzPRE\ngA6CIAiCYUgE6CAIgiAYhkSADoIgCIJhSAToIAiCIBiGxD7oWRxJCwNXkZKAPEfKRz2D45mkTwE/\nID3UXWz7zNK5w4CDgfeAG22f0AHpLdGezx9NcmT7iO3X262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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e5728c668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 2* Ridge\n",
    "ridge = RidgeCV(alphas = [0.01, 0.03, 0.06, 0.1, 0.3, 0.6, 1, 3, 6, 10, 30, 60])\n",
    "ridge.fit(X_train, y_train)\n",
    "alpha = ridge.alpha_\n",
    "print(\"Best alpha :\", alpha)\n",
    "\n",
    "print(\"Try again for more precision with alphas centered around \" + str(alpha))\n",
    "ridge = RidgeCV(alphas = [alpha * .6, alpha * .65, alpha * .7, alpha * .75, alpha * .8, alpha * .85, \n",
    "                          alpha * .9, alpha * .95, alpha, alpha * 1.05, alpha * 1.1, alpha * 1.15,\n",
    "                          alpha * 1.25, alpha * 1.3, alpha * 1.35, alpha * 1.4], \n",
    "                cv = 10)\n",
    "ridge.fit(X_train, y_train)\n",
    "alpha = ridge.alpha_\n",
    "print(\"Best alpha :\", alpha)\n",
    "\n",
    "print(\"Ridge RMSE on Training set :\", rmse_cv_train(ridge).mean())\n",
    "print(\"Ridge RMSE on Test set :\", rmse_cv_test(ridge).mean())\n",
    "y_train_rdg = ridge.predict(X_train)\n",
    "y_test_rdg = ridge.predict(X_test)\n",
    "\n",
    "# Plot residuals\n",
    "plt.scatter(y_train_rdg, y_train_rdg - y_train, c = \"blue\", marker = \"s\", label = \"Training data\")\n",
    "plt.scatter(y_test_rdg, y_test_rdg - y_test, c = \"lightgreen\", marker = \"s\", label = \"Validation data\")\n",
    "plt.title(\"Linear regression with Ridge regularization\")\n",
    "plt.xlabel(\"Predicted values\")\n",
    "plt.ylabel(\"Residuals\")\n",
    "plt.legend(loc = \"upper left\")\n",
    "plt.hlines(y = 0, xmin = 10.5, xmax = 13.5, color = \"red\")\n",
    "plt.show()\n",
    "\n",
    "# Plot predictions\n",
    "plt.scatter(y_train_rdg, y_train, c = \"blue\", marker = \"s\", label = \"Training data\")\n",
    "plt.scatter(y_test_rdg, y_test, c = \"lightgreen\", marker = \"s\", label = \"Validation data\")\n",
    "plt.title(\"Linear regression with Ridge regularization\")\n",
    "plt.xlabel(\"Predicted values\")\n",
    "plt.ylabel(\"Real values\")\n",
    "plt.legend(loc = \"upper left\")\n",
    "plt.plot([10.5, 13.5], [10.5, 13.5], c = \"red\")\n",
    "plt.show()\n",
    "\n",
    "# Plot important coefficients\n",
    "coefs = pd.Series(ridge.coef_, index = X_train.columns)\n",
    "print(\"Ridge picked \" + str(sum(coefs != 0)) + \" features and eliminated the other \" +  \\\n",
    "      str(sum(coefs == 0)) + \" features\")\n",
    "imp_coefs = pd.concat([coefs.sort_values().head(10),\n",
    "                     coefs.sort_values().tail(10)])\n",
    "imp_coefs.plot(kind = \"barh\")\n",
    "plt.title(\"Coefficients in the Ridge Model\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_cell_guid": "6e4193a5-7734-be2d-4ad7-460211cbd65e"
   },
   "source": [
    "We're getting a much better RMSE result now that we've added regularization. The very small difference between training and test results indicate that we eliminated most of the overfitting. Visually, the graphs seem to confirm that idea.  \n",
    "\n",
    "Ridge used almost all of the existing features."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_cell_guid": "2da33461-fb1a-c09a-b0fe-d20e8c8f52e3"
   },
   "source": [
    "**3* Linear Regression with Lasso regularization (L1 penalty)**\n",
    "\n",
    "LASSO stands for *Least Absolute Shrinkage and Selection Operator*. It is an alternative regularization method, where we simply replace the square of the weights by the sum of the absolute value of the weights. In contrast to L2 regularization, L1 regularization yields sparse feature vectors : most feature weights will be zero. Sparsity can be useful in practice if we have a high dimensional dataset with many features that are irrelevant.  \n",
    "\n",
    "We can suspect that it should be more efficient than Ridge here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "_cell_guid": "8525724a-fb77-66d4-e06f-f3365fbd8ec3"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best alpha : 0.0006\n",
      "Try again for more precision with alphas centered around 0.0006\n",
      "Best alpha : 0.0006\n",
      "Lasso RMSE on Training set : 0.114111508375\n",
      "Lasso RMSE on Test set : 0.115832132218\n"
     ]
    },
    {
     "data": {
      "image/png": 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QvhtNf6AFi2ZIYmV4d1abKjQTPCsru8uz+WhqAz0VuF0THD333WiNR9MTtGDR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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e57439ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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HbdiwP8Gj0WiaMPHxiaSlWYFfvbbVR1hsmFvItKqsJnv4PMKDvsNU42QOtzGd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\nDgb2OTjc4kqewQXDCPNCUrUBE1i0qImylDgSBbC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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e56efe9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lasso picked 110 features and eliminated the other 209 features\n"
     ]
    },
    {
     "data": {
      "image/png": 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1/wwcQBxjmkIus8iXbk1ETA8tKl+/B95X6v3Adishk28BZ9Wcc7GnJspSk/J8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\nSZIkfUg66CRJkiTpQ/4H/8p6BLiehYIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e57366908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 3* Lasso\n",
    "lasso = LassoCV(alphas = [0.0001, 0.0003, 0.0006, 0.001, 0.003, 0.006, 0.01, 0.03, 0.06, 0.1, \n",
    "                          0.3, 0.6, 1], \n",
    "                max_iter = 50000, cv = 10)\n",
    "lasso.fit(X_train, y_train)\n",
    "alpha = lasso.alpha_\n",
    "print(\"Best alpha :\", alpha)\n",
    "\n",
    "print(\"Try again for more precision with alphas centered around \" + str(alpha))\n",
    "lasso = LassoCV(alphas = [alpha * .6, alpha * .65, alpha * .7, alpha * .75, alpha * .8, \n",
    "                          alpha * .85, alpha * .9, alpha * .95, alpha, alpha * 1.05, \n",
    "                          alpha * 1.1, alpha * 1.15, alpha * 1.25, alpha * 1.3, alpha * 1.35, \n",
    "                          alpha * 1.4], \n",
    "                max_iter = 50000, cv = 10)\n",
    "lasso.fit(X_train, y_train)\n",
    "alpha = lasso.alpha_\n",
    "print(\"Best alpha :\", alpha)\n",
    "\n",
    "print(\"Lasso RMSE on Training set :\", rmse_cv_train(lasso).mean())\n",
    "print(\"Lasso RMSE on Test set :\", rmse_cv_test(lasso).mean())\n",
    "y_train_las = lasso.predict(X_train)\n",
    "y_test_las = lasso.predict(X_test)\n",
    "\n",
    "# Plot residuals\n",
    "plt.scatter(y_train_las, y_train_las - y_train, c = \"blue\", marker = \"s\", label = \"Training data\")\n",
    "plt.scatter(y_test_las, y_test_las - y_test, c = \"lightgreen\", marker = \"s\", label = \"Validation data\")\n",
    "plt.title(\"Linear regression with Lasso regularization\")\n",
    "plt.xlabel(\"Predicted values\")\n",
    "plt.ylabel(\"Residuals\")\n",
    "plt.legend(loc = \"upper left\")\n",
    "plt.hlines(y = 0, xmin = 10.5, xmax = 13.5, color = \"red\")\n",
    "plt.show()\n",
    "\n",
    "# Plot predictions\n",
    "plt.scatter(y_train_las, y_train, c = \"blue\", marker = \"s\", label = \"Training data\")\n",
    "plt.scatter(y_test_las, y_test, c = \"lightgreen\", marker = \"s\", label = \"Validation data\")\n",
    "plt.title(\"Linear regression with Lasso regularization\")\n",
    "plt.xlabel(\"Predicted values\")\n",
    "plt.ylabel(\"Real values\")\n",
    "plt.legend(loc = \"upper left\")\n",
    "plt.plot([10.5, 13.5], [10.5, 13.5], c = \"red\")\n",
    "plt.show()\n",
    "\n",
    "# Plot important coefficients\n",
    "coefs = pd.Series(lasso.coef_, index = X_train.columns)\n",
    "print(\"Lasso picked \" + str(sum(coefs != 0)) + \" features and eliminated the other \" +  \\\n",
    "      str(sum(coefs == 0)) + \" features\")\n",
    "imp_coefs = pd.concat([coefs.sort_values().head(10),\n",
    "                     coefs.sort_values().tail(10)])\n",
    "imp_coefs.plot(kind = \"barh\")\n",
    "plt.title(\"Coefficients in the Lasso Model\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_cell_guid": "5d979d30-a58b-cdb5-18cd-78842fa0e42e"
   },
   "source": [
    "RMSE results are better both on training and test sets. The most interesting thing is that Lasso used only one third of the available features. Another interesting tidbit : it seems to give big weights to Neighborhood categories, both in positive and negative ways. Intuitively it makes sense, house prices change a whole lot from one neighborhood to another in the same city.  \n",
    "\n",
    "The \"MSZoning_C (all)\" feature seems to have a disproportionate impact compared to the others. It is defined as *general zoning classification : commercial*. It seems a bit weird to me that having your house in a mostly commercial zone would be such a terrible thing."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_cell_guid": "80ffe575-2022-2802-9994-858c06786e68"
   },
   "source": [
    "**4* Linear Regression with ElasticNet regularization (L1 and L2 penalty)**\n",
    "\n",
    "ElasticNet is a compromise between Ridge and Lasso regression. It has a L1 penalty to generate sparsity and a L2 penalty to overcome some of the limitations of Lasso, such as the number of variables (Lasso can't select more features than it has observations, but it's not the case here anyway)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "_cell_guid": "4a641b34-5bdc-a183-c442-6cc91c506e86"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.5/site-packages/sklearn/linear_model/coordinate_descent.py:479: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best l1_ratio : 1.0\n",
      "Best alpha : 0.0006\n",
      "Try again for more precision with l1_ratio centered around 1.0\n",
      "Best l1_ratio : 1.0\n",
      "Best alpha : 0.0006\n",
      "Now try again for more precision on alpha, with l1_ratio fixed at 1.0 and alpha centered around 0.0006\n",
      "Best l1_ratio : 1.0\n",
      "Best alpha : 0.0006\n",
      "ElasticNet RMSE on Training set : 0.114111508375\n",
      "ElasticNet RMSE on Test set : 0.115832132218\n"
     ]
    },
    {
     "data": {
      "image/png": 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tWDRHHVaGd2Wlj0/40PGb3STW00zw6LUBt4krl9jSe05/XZFYcyRowaI56rDP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\nko0iMh335HIElwr+aKFs7MfOHuB/ACcD+4HNqvqnxRrL4dhZIuO5Ehg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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e56fa24e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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iABYvDqM4ocZNw4B+jGY378c+QXRuOdbYMFbMOoP4IVeyLt5OVlaNEXC4C8jw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\nRCQS/w9Tpv0Kbh7JDQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e56f5b0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ElasticNet picked 110 features and eliminated the other 209 features\n"
     ]
    },
    {
     "data": {
      "image/png": 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J0pihnkEPKUWd60TirPUw4HLiKNTbU9tnM6nPyphjbc9dhFUut71cKf8YcTTs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\nHk+pxSSZSFLqMxktg+igAb4H7EIkl9ifEC55e7n2ZiL8CAD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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e56eb6a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 4* ElasticNet\n",
    "elasticNet = ElasticNetCV(l1_ratio = [0.1, 0.3, 0.5, 0.6, 0.7, 0.8, 0.85, 0.9, 0.95, 1],\n",
    "                          alphas = [0.0001, 0.0003, 0.0006, 0.001, 0.003, 0.006, \n",
    "                                    0.01, 0.03, 0.06, 0.1, 0.3, 0.6, 1, 3, 6], \n",
    "                          max_iter = 50000, cv = 10)\n",
    "elasticNet.fit(X_train, y_train)\n",
    "alpha = elasticNet.alpha_\n",
    "ratio = elasticNet.l1_ratio_\n",
    "print(\"Best l1_ratio :\", ratio)\n",
    "print(\"Best alpha :\", alpha )\n",
    "\n",
    "print(\"Try again for more precision with l1_ratio centered around \" + str(ratio))\n",
    "elasticNet = ElasticNetCV(l1_ratio = [ratio * .85, ratio * .9, ratio * .95, ratio, ratio * 1.05, ratio * 1.1, ratio * 1.15],\n",
    "                          alphas = [0.0001, 0.0003, 0.0006, 0.001, 0.003, 0.006, 0.01, 0.03, 0.06, 0.1, 0.3, 0.6, 1, 3, 6], \n",
    "                          max_iter = 50000, cv = 10)\n",
    "elasticNet.fit(X_train, y_train)\n",
    "if (elasticNet.l1_ratio_ > 1):\n",
    "    elasticNet.l1_ratio_ = 1    \n",
    "alpha = elasticNet.alpha_\n",
    "ratio = elasticNet.l1_ratio_\n",
    "print(\"Best l1_ratio :\", ratio)\n",
    "print(\"Best alpha :\", alpha )\n",
    "\n",
    "print(\"Now try again for more precision on alpha, with l1_ratio fixed at \" + str(ratio) + \n",
    "      \" and alpha centered around \" + str(alpha))\n",
    "elasticNet = ElasticNetCV(l1_ratio = ratio,\n",
    "                          alphas = [alpha * .6, alpha * .65, alpha * .7, alpha * .75, alpha * .8, alpha * .85, alpha * .9, \n",
    "                                    alpha * .95, alpha, alpha * 1.05, alpha * 1.1, alpha * 1.15, alpha * 1.25, alpha * 1.3, \n",
    "                                    alpha * 1.35, alpha * 1.4], \n",
    "                          max_iter = 50000, cv = 10)\n",
    "elasticNet.fit(X_train, y_train)\n",
    "if (elasticNet.l1_ratio_ > 1):\n",
    "    elasticNet.l1_ratio_ = 1    \n",
    "alpha = elasticNet.alpha_\n",
    "ratio = elasticNet.l1_ratio_\n",
    "print(\"Best l1_ratio :\", ratio)\n",
    "print(\"Best alpha :\", alpha )\n",
    "\n",
    "print(\"ElasticNet RMSE on Training set :\", rmse_cv_train(elasticNet).mean())\n",
    "print(\"ElasticNet RMSE on Test set :\", rmse_cv_test(elasticNet).mean())\n",
    "y_train_ela = elasticNet.predict(X_train)\n",
    "y_test_ela = elasticNet.predict(X_test)\n",
    "\n",
    "# Plot residuals\n",
    "plt.scatter(y_train_ela, y_train_ela - y_train, c = \"blue\", marker = \"s\", label = \"Training data\")\n",
    "plt.scatter(y_test_ela, y_test_ela - y_test, c = \"lightgreen\", marker = \"s\", label = \"Validation data\")\n",
    "plt.title(\"Linear regression with ElasticNet regularization\")\n",
    "plt.xlabel(\"Predicted values\")\n",
    "plt.ylabel(\"Residuals\")\n",
    "plt.legend(loc = \"upper left\")\n",
    "plt.hlines(y = 0, xmin = 10.5, xmax = 13.5, color = \"red\")\n",
    "plt.show()\n",
    "\n",
    "# Plot predictions\n",
    "plt.scatter(y_train, y_train_ela, c = \"blue\", marker = \"s\", label = \"Training data\")\n",
    "plt.scatter(y_test, y_test_ela, c = \"lightgreen\", marker = \"s\", label = \"Validation data\")\n",
    "plt.title(\"Linear regression with ElasticNet regularization\")\n",
    "plt.xlabel(\"Predicted values\")\n",
    "plt.ylabel(\"Real values\")\n",
    "plt.legend(loc = \"upper left\")\n",
    "plt.plot([10.5, 13.5], [10.5, 13.5], c = \"red\")\n",
    "plt.show()\n",
    "\n",
    "# Plot important coefficients\n",
    "coefs = pd.Series(elasticNet.coef_, index = X_train.columns)\n",
    "print(\"ElasticNet picked \" + str(sum(coefs != 0)) + \" features and eliminated the other \" +  str(sum(coefs == 0)) + \" features\")\n",
    "imp_coefs = pd.concat([coefs.sort_values().head(10),\n",
    "                     coefs.sort_values().tail(10)])\n",
    "imp_coefs.plot(kind = \"barh\")\n",
    "plt.title(\"Coefficients in the ElasticNet Model\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_cell_guid": "61b7db78-5628-75e9-016a-067004049ddc"
   },
   "source": [
    "The optimal L1 ratio used by ElasticNet here is equal to 1, which means it is exactly equal to the Lasso regressor we used earlier (and had it been equal to 0, it would have been exactly equal to our Ridge regressor). The model didn't need any L2 regularization to overcome any potential L1 shortcoming."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_cell_guid": "a497362f-bad8-99ad-2320-d651435723d3"
   },
   "source": [
    "Note : I tried to remove the \"MSZoning_C (all)\" feature, it resulted in a slightly worse CV score, but slightly better public LB score."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "_cell_guid": "9bce5b62-c17b-d1cf-e3e6-2b88dbbc9d7f"
   },
   "source": [
    "**Conclusion**  \n",
    "\n",
    "Putting time and effort into preparing the dataset and optimizing the regularization resulted in a decent score, better than some public scripts which use algorithms that historically perform better in Kaggle contests, like Random Forests. Being fairly new to the world of machine learning contests, I will appreciate any constructive pointer to improve, and I thank you for your time."
   ]
  }
 ],
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